LIFE LEXICON
Release 26 beta 4, 2017 August 23 (TBD)
ASCII version
INTRODUCTION
This is a lexicon of terms relating to John Horton Conway's
Game of Life. It is also available in single-page and multipage
HTML versions.
This lexicon was originally compiled between 1997 and 2006 by
Stephen A. Silver, and was updated in 2016-17 by Dave Greene. See
below for additional credits.
The latest versions of this lexicon (both HTML and ASCII) can be
found at the Life Lexicon Home Page, http://conwaylife.com/ref/lexicon/.
CREDITS
The largest single source for the early versions of this lexicon was
a glossary compiled by Alan Hensel "with indispensable help from John
Conway, Dean Hickerson, David Bell, Bill Gosper, Bob Wainwright, Noam
Elkies, Nathan Thompson, Harold McIntosh, and Dan Hoey".
Other sources include the works listed in the bibliography at the
end of this lexicon, as well as pattern collections by Alan Hensel and
David Bell (and especially Dean Hickerson's file stamp.l in the latter
collection), and the web sites of Mark Niemiec, Paul Callahan, Achim
Flammenkamp, Robert Wainwright and Heinrich Koenig. Recent releases
also use a lot of information from Dean Hickerson's header to his
1995 stamp file (http://conwaylife.com/ref/DRH/stamps.html).
Most of the information on recent results is from the discoverers
themselves, or from Nathaniel Johnston's excellent resources at
http://www.conwaylife.com, including both the LifeWiki and the
discussion forums.
The following people all provided useful comments on earlier releases
of this lexicon: David Bell, Nicolay Beluchenko, Johan Bontes, Scot
Ellison, Nick Gotts, Ivan Fomichev, Dave Greene, Alan Hensel, Dean
Hickerson, Dieter Leithner, Mark Niemiec, Gabriel Nivasch, Andrzej
Okrasinski, Peter Rott, Chris Rowett, Tony Smith, Ken Takusagawa, Andrew
Trevorrow, Malcolm Tyrrell, and the user with the handle 'thunk' on the
conwaylife.com forums.
The format, errors, use of British English and anything else you
might want to complain about are by Stephen Silver -- except that in
editions later than Version 25, many details besides the British English
may well be Dave Greene's fault.
COPYING
This lexicon is copyright (C) Stephen Silver, 1997-2017. It may be
freely copied and/or modified as long as due credit is given. This
includes not just credit to those who have contributed in some way to
the present version (see above), but also credit to those who have made
any modifications.
LEXICOGRAPHIC ORDER
I have adopted the following convention: all characters (including
spaces) other than letters and digits are ignored for the purposes of
ordering the entries in this lexicon. (Many terms are used by some
people as a single word, with or without a hyphen, and by others as two
words. My convention means that I do not have to list these in two
separate places. Indeed, I list them only once, choosing whichever
form seems most common or sensible.) Digits lexicographically precede
letters.
FORMAT
The format used in the ASCII version of this lexicon is loosely
based on that of the Jargon File. In particular, the keywords are
enclosed in colons and selected references to them are enclosed in
curly brackets. The curly brackets will not be of much use unless
you have a programmable text editor, in which case you could program
it to jump from a reference to the corresponding definition when you
hit a certain key. (The file lifelex.el, which you should have
received with this lexicon, provides such a facility for GNU Emacs.)
If you don't want the curly brackets you can safely remove them with
two find and replace operations, since they are not used for any other
purpose in this file. The colons are more generally useful. For
example, a search for ":foo" will take you straight to the definition
of the first word beginning with "foo" (or at least it would if there
were any).
The diagrams in this lexicon are in a very standard format. You
should be able to simply copy a pattern, paste it into a new file and
run it in your favourite Life program. If you use Johan Bontes' Life32,
Mirek Wojtowicz' MCell or Andrew Trevorrow and Tomas Rokicki's Golly
then you can, of course, paste the pattern directly into the Life
program. If you view this lexicon in GNU Emacs and use lifelex.el then
you should be able to load a pattern into your Life program with a
single keypress, without needing to copy or paste.
The diagrams use an asterisk to represent a live cell. If this looks
ugly with the font you use then you can change to O or o with a global
replace. I have restricted myself to diagrams of size 64x64 or less.
Most definitions that have a diagram have also some data in brackets
after the keyword. Oscillators are marked as pn (where n is a positive
integer), meaning that the period is n (p1 indicates a still life).
Wicks are marked in the same way but with the word "wick" added. For
spaceships the speed (as a fraction of c, the speed of light), the
direction and the period are given. Fuses are marked with speed and
period and have the word "fuse" added. Wicks and fuses are infinite in
extent and so have necessarily been truncated, with the ends stabilized
wherever practical.
SCOPE
This lexicon covers only Conway's Life, and provides no information
about other cellular automata. David Bell has written articles on
two other interesting cellular automata: HighLife (which is similar
to Life, but has a tiny replicator) and Day & Night (which is very
different, but exhibits many of the same phenomena). These articles
can be found on his website (http://www.canb.auug.org.au/~dbell/).
ERRORS AND OMISSIONS
If you find any errors (including typos) or serious omissions, then
please email b3s23life[at]gmail.com with the details. This email
address is currently monitored by Dave Greene, who has completed the
long-delayed update from Release 25 to Release 26.
NAMES
When deciding whether to use full or abbreviated forms of forenames
I have tried, wherever possible, to follow the usage of the person
concerned.
QUOTE
Every other author may aspire to praise; the lexicographer can only
hope to escape reproach. -- Samuel Johnson, 1775
DEDICATION
This lexicon is dedicated to the memory of Dieter Leithner, who died
on 26 February 1999.
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:0hd Demonoid: See {Demonoid}.
:101: (p5) Found by Achim Flammenkamp in August 1994. The name was
suggested by Bill Gosper, noting that the {phase} shown below
displays the period in binary.
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:10hd Demonoid: See {Demonoid}.
:119P4H1V0: (c/4 orthogonally, p4) A {spaceship} discovered by Dean
Hickerson in December 1989, the first spaceship of its kind to be
found. Hickerson then found a small tagalong for this spaceship which
could be attached to one side or both. These three variants of
119P4H1V0 were the only known c/4 orthogonal spaceships until July
1992 when Hartmut Holzwart discovered a larger spaceship, 163P4H1V0.
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:1-2-3: (p3) Found by Dave Buckingham, August 1972. This is one of only
three essentially different p3 {oscillator}s with only three cells in
the {rotor}. The others are {stillater} and {cuphook}.
..**......
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:1-2-3-4: (p4) See also {Achim's p4}.
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:135-degree MWSS-to-G: The following {converter}, discovered by
Matthias Merzenich in July 2013. It accepts an MWSS as input, and
produces an output glider traveling at a 135-degree angle relative to
the input direction.
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:14-ner: = {fourteener}
:17c/45 spaceship: A {spaceship} travelling at seventeen forty-fifths
of the {speed of light}. This was the first known {macro-spaceship}
speed. See {Caterpillar} for details.
:180-degree kickback: The only other two-glider collision besides the
standard {kickback} that produces a clean 180-degree output glider.
It is occasionally useful in {glider synthesis}, but is rarely used
in {signal} circuitry or in {self-supporting} patterns like the
{Caterpillar} or {Centipede}, because 90-degree collisions are
generally much easier to arrange.
.*.
*..
***
...
...
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*.*
..*
:1G seed: See {seed}.
:(23,5)c/79: The rate of travel of the {Herschel climber} reaction used
in the {self-supporting} {waterbear} {knightship}.
:(23,5)c/79 Herschel climber: The following glider-supported reaction
used in the {waterbear}, which can be repeated every 79 ticks, moving
the Herschel 23 cells to the right and 5 cells upward, and releasing
two gliders to the northwest and southwest. As the diagram shows, it
is possible to substitute a loaf or other still lifes for some or all
of the support gliders. This fact is used to advantage at the front
end of the {waterbear} spaceship.
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:24-cell quadratic growth: A 39786x143 {quadratic growth} pattern found
by Michael Simkin in October 2014, two days after {26-cell quadratic
growth} and a week before {switch-engine ping-pong}.
:25-cell quadratic growth: A 25-cell quadratic growth pattern found by
Michael Simkin on October 2014, with a bounding box of 21372x172. It
was the smallest-population quadratic growth pattern for two days,
until the discovery of {24-cell quadratic growth}. It superseded
{26-cell quadratic growth}, which had held the record for eight
years.
:25P3H1V0.1: (c/3 orthogonally, p3) A spaceship discovered by David
Bell, with a minimum of 25 cells -- the lowest number of cells known
for any c/3 spaceship. See also {edge-repair spaceship} for a very
similar c/3 spaceship with a minimumm population of 26.
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.****...........
*...*...........
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:25P3H1V0.2: (c/3 orthogonally, p3) A spaceship discovered by Dean
Hickerson in August 1989. It was the first c/3 spaceship to be
discovered. In terms of its 25 cells, it is tied with {25P3H1V0.1} as
the smallest c/3 spaceship. Unlike 25P3H1V0.1, it has a population
of 25 in all of its phases, as well as a smaller bounding box.
Martin Grant discovered a glider synthesis for 25P3H1V0.2 on 6 January
2015.
.......**.*.....
....**.*.**.***.
.****..**......*
*....*...*...**.
.**.............
:26-cell quadratic growth: a quadratic growth pattern found by Nick
Gotts in March 2006, using ideas found in {metacatacryst} and {Gotts
dots}. It held the record for the smallest-population quadratic
growth pattern for eight years, until it was surpassed by {25-cell
quadratic growth}.
:295P5H1V1: (c/5 diagonally, p5) The first spaceship of its type to be
discovered, found by Jason Summers on 22 November 2000.
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:2c/3: Two thirds of the speed of light -- the speed of signals in a
{2c/3 wire}, or of some {against the grain} {negative spaceship}
signals in the {stripes} {agar}.
:2c/5 spaceship: A {spaceship} travelling at two fifths of the {speed
of light}. The only such spaceships that are currently known travel
orthogonally. Examples include {30P5H2V0}, {44P5H2V0}, {60P5H2V0},
and {70P5H2V0}. At the time of this writing (August 2017) only
30P5H2V0 and 60P5H2V0 have known {glider synthesis} {recipe}s.
:2c/7 spaceship: A {spaceship} travelling at two sevenths of the {speed
of light}. The only such spaceships that are currently known travel
orthogonally. The first to be found was the {weekender}, found by
David Eppstein in January 2000. See also {weekender distaff}.
:2 eaters: = {two eaters}
:30P5H2V0: (2c/5 orthogonally, p5) A spaceship discovered by Paul Tooke
on 7 December 2000. With just 30 cells, it is currently the smallest
known 2c/5 spaceship. A {glider synthesis} for 30P5H2V0 was found by
Martin Grant in January 2015, based on a predecessor by Tanner
Jacobi.
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:31c/240: The rate of travel of the {31c/240 Herschel-pair climber}
reaction, and {Caterpillar}-type spaceships based on that reaction.
Each {Herschel} travels 31 cells orthogonally every 240 {tick}s.
:31c/240 Herschel-pair climber: The mechanism defining the rate of
travel of the {Centipede} and {shield bug} spaceships. Compare {pi
climber}. It consists of a pair of {Herschel}s climbing two parallel
chains of blocks. Certain spacings between the block chains allow
gliders from each Herschel to delete the extra ash objects produced
by the other Herschel. Two more gliders escape, one to each side,
leaving only an exact copy of the original block chains, but shifted
forward by 9 cells:
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:3c/7 spaceship: A {spaceship} travelling at three sevenths of the
{speed of light}. The only such spaceships that are currently known
travel orthogonally. The first to be found was the {spaghetti
monster}, found by Tim Coe in June 2016.
:44P5H2V0: (2c/5 orthogonally, p5) A spaceship discovered by Dean
Hickerson on 23 July 1991, the first 2c/5 spaceship to be found.
Small {tagalong}s were found by Robert Wainwright and David Bell that
allowed the creation of arbitrarily large 2c/5 spaceships. These were
the only known 2c/5 spaceships until the discovery of {70P5H2V0} in
December 1992.
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:45-degree LWSS-to-G: = {45-degree MWSS-to-G}.
:45-degree MWSS-to-G: The following small {converter}, which accepts an
MWSS or LWSS as input and produces an output glider traveling at a
45-degree angle relative to the input direction.
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:4-8-12 diamond: The following {pure glider generator}.
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:4 boats: (p2)
...*....
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:4F: = {Fast Forward Force Field}. This term is no longer in common
use.
:56P6H1V0: (c/6 orthogonally, p6) A 56-cell spaceship discovered by
Hartmut Holzwart in 2009, the smallest known c/6 orthogonal spaceship
as of this writing (August 2017).
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:58P5H1V1: (c/5 diagonally, p5) A spaceship discovered by Matthias
Merzenich on 5 September 2010. In terms of its minimum population of
58 cells it is the smallest known c/5 diagonal spaceship. It provides
sparks at its trailing edge which can perturb gliders, and this
property was used to create the first c/5 diagonal puffers. These
sparks also allow the attachment of tagalongs which was used to
create the first c/5 diagonal wickstretcher in January 2011.
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:60P5H2V0: (2c/5 orthogonally, c5) A 60-cell spaceship discovered by
Tim Coe in May 1996. It was the first non-c/2 orthogonal spaceship
to be successfully constructed via {glider synthesis}.
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:67P5H1V1: (c/5 diagonally, p5) A spaceship discovered by Nicolay
Beluchenko in July 2006. It was the smallest known c/5 diagonal
spaceship until the discovery of {58P5H1V1} in September 2010.
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:70P5H2V0: (2c/5 orthogonally, c/5) A spaceship discovered by Hartmut
Holzwart on 5 December 1992.
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:7x9 eater: a high-{clearance} {eater5} variant that can suppress
passing gliders in tight spaces, such as on the inside corner of an
{R64} {Herschel conduit}. Like the eater5 and {sidesnagger}, the 7x9
eater is able to eat gliders coming from two directions, though this
ability is not commonly used.
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:83P7H1V1: = {lobster}
:86P5H1V1: (c/5 diagonally, p5) A spaceship discovered by Jason Summers
on January 8, 2005. It was the smallest known c/5 diagonal spaceship
until the discovery of {67P5H1V1} in July 2006.
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:90-degree kickback: See {kickback}.
:9hd: separated by 9 {half diagonal}s.
:Achim's p144: (p144) This was found (minus the blocks shown below) on
a cylinder of width 22 by Achim Flammenkamp in July 1994. Dean
Hickerson reduced it to a finite form using {figure-8}s the same day.
The neater finite form shown here - replacing the figure-8s with
blocks - was found by David Bell in August 1994. See {factory} for a
use of this oscillator.
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:Achim's p16: (p16) Found by Achim Flammenkamp, July 1994.
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:Achim's p4: (p4) Dave Buckingham found this in a less compact form
(using two halves of {sombreros}) in 1976. The form shown here was
found by Achim Flammenkamp in 1988. The {rotor} is two copies of the
rotor of {1-2-3-4}, so the oscillator is sometimes called the "dual
1-2-3-4".
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:Achim's p5: = {pseudo-barberpole}
:Achim's p8: (p8) Found by Achim Flammenkamp, July 1994.
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:acorn: (stabilizes at time 5206) A {methuselah} found by Charles
Corderman.
.*.....
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**..***
:A for all: (p6) Found by Dean Hickerson in March 1993.
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:against the grain: term used for {negative spaceship}s traveling in
{zebra stripes} agar, perpendicular to the stripes, and also for
{against-the-grain grey ship}s.
Below is a sample {signal}, found by Hartmut Holzwart in April
2006, that travels against the grain at {2c/3}. This "negative
spaceship" travels upward and will quickly reach the edge of the
finite patch of stabilized agar shown here.
...*..*..*..*..*..*..*..*..*..*..*...
.***********************************.
*...................................*
.***********************************.
.....................................
.***********************************.
*...................................*
.***********************************.
.....................................
.***********************************.
*...................................*
.***********************************.
.....................................
.***********************************.
*...................................*
.*****************..****************.
.....................................
.***************......**************.
*...............*....*..............*
.****************....***************.
.....................................
.*************...****...************.
*.................**................*
.************............***********.
.............*..........*............
.**************........*************.
*..............*......*.............*
.***************......**************.
..........**....*....*....**.........
.*******......****..****......******.
*.......*...**...*..*...**...*......*
.*******.........*..*.........******.
.........*.....*......*.....*........
.*********......*....*......********.
*.........*....**.**.**....*........*
.***********....*....*....**********.
............**....**....**...........
.*******..***.*..*..*..*.***..******.
*..............***..***.............*
.*****......***.*....*.***......****.
......*....*..............*....*.....
.******........*......*........*****.
*......*...**..*..**..*..**...*.....*
.********.....*.**..**.*.....*******.
.........*..*.**......**.*..*........
.*********...**........**...********.
*..........*..............*.........*
.****************....***************.
.................****................
.*****************..****************.
*...................................*
.***********************************.
...*..*..*..*..*..*..*..*..*..*..*...
Holzwart proved in 2006 that 2c/3 is the maximum speed at which
signals can move non-destructively against the grain through zebra
stripes agar.
:against-the-grain grey ship: A {grey ship} in which the region of
density 1/2 consists of lines of ON cells lying perpendicular to the
direction in which the spaceship moves. See also {with-the-grain
grey ship}.
:agar: Any pattern covering the whole plane that is periodic in both
space and time. The simplest (nonempty) agar is the {stable} one
extended by the known {spacefiller}s. For some more examples see
{chicken wire}, {houndstooth agar}, {onion rings}, {squaredance} and
{Venetian blinds}. Tiling the plane with the pattern O......O
produces another interesting example: a p6 agar which has a phase of
{density} 3/4, which is the highest yet obtained for any phase of an
oscillating pattern.
:aircraft carrier: (p1) This is the smallest {still life} that has more
than one {island}.
**..
*..*
..**
:airforce: (p7) Found by Dave Buckingham in 1972. The rotor consists
of two copies of that used in the {burloaferimeter}.
.......*......
......*.*.....
.......*......
..............
.....*****....
....*.....*.**
...*.**...*.**
...*.*..*.*...
**.*...**.*...
**.*.....*....
....*****.....
..............
......*.......
.....*.*......
......*.......
:AK47 reaction: The following reaction (found by Rich Schroeppel and
Dave Buckingham) in which a honey farm predecessor, catalysed by an
eater and a block, reappears at another location 47 generations
later, having produced a glider and a traffic light. This is the
basis of a very small (but {pseudo}) p94 glider gun found by Paul
Callahan in July 1994, and was in 1990 the basis for the Dean
Hickerson's construction of the first {true} p94 gun. (This latter
gun was enormous, and has now been superseded by comparatively small
{Herschel loop} guns.)
.....*....
....*.*...
...*...*..
...*...*..
...*...*..
....*.*...
.....*....
..........
..**......
...*......
***.....**
*.......**
:AK94 gun: The smallest known gun using the {AK47 reaction}, found by
Mike Playle in May 2013 using his {Bellman} program.
.......*.......*.......**.............
.......***.....***.....**.............
..........*.......*...................
.........**......**................**.
..............................**..*..*
..............................*.*..**.
.................................**...
.....*............................*...
.....***..........................*.**
........*......................**.*..*
.......**......................**.**..
......................................
......................................
.................*....................
..**.**.........*.*..........**.......
*..*.**........*...*.........*........
**.*...........*...*..........***.....
...*...........*...*............*.....
...**...........*.*...................
.**..*.*.........*....................
*..*..**..............................
.**................**.................
...................*..................
.............**.....***...............
.............**.......*...............
:Al Jolson: = {Jolson}
:almosymmetric: (p2) Found in 1971.
....*....
**..*.*..
*.*......
.......**
.*.......
*......*.
**.*.*...
.....*...
:ambidextrous: a type of {Herschel transceiver} where the {receiver}
can be used in either of two mirror-image orientations. See also
{chirality}.
:anteater: A pattern that consumes {ants}. Matthias Merzenich
discovered a c/5 anteater on 15 April 2011. See {wavestretcher} for
details.
:antlers: = {moose antlers}
:ants: (p5 wick) The standard form is shown below. It is also possible
for any ant to be displaced by one or two cells relative to either or
both of its neighbouring ants. Dean Hickerson found {fencepost}s for
both ends of this wick in October 1992 and February 1993. See
{electric fence}, and also {wickstretcher}.
**...**...**...**...**...**...**...**...**..
..**...**...**...**...**...**...**...**...**
..**...**...**...**...**...**...**...**...**
**...**...**...**...**...**...**...**...**..
:antstretcher: Any {wickstretcher} that stretches {ants}. Nicolay
Beluchenko and Hartmut Holzwart constructed the following small
{extensible} antstretcher in January 2006:
......................................................**.......
.....................................................**........
...............................................**.....*........
..............................................**.....**........
................................................*....*.*..**...
..................................................**...**.****.
..................................................**..........*
..............................................................*
........................................................*......
..........................................................**...
...............................................................
..........................................................***..
.........................................................**..*.
...............................**..........................*...
..............................**...............................
...............................*.*...................***..*....
..........................*....***...................*..***....
.........................*****.***..*.**................**.....
.........................*..**......*...**.**.........**.**....
...................................*....**...**.**.......**....
...........................**..**.**..**.....**...**.*.*.......
...................................*.......**.....**...........
.....................***...*.....**.............**....*........
.....................*.....*..*.**...................*.........
......................*...**.*.................................
.........................**...*.*..............................
.............***..........*....................................
.............*.....***..**.....................................
..............*..**.***.**.....................................
................*..........*...................................
.................*.*.**....*...................................
...................**.*........................................
.................**...*.*......................................
................**.............................................
..................*............................................
...............**..............................................
..............***..............................................
.............**.*..............................................
............****.*.............................................
.................***...........................................
..................**...........................................
..........***.**...............................................
.........*...***...............................................
............***................................................
........*.*.*..................................................
.......****....................................................
.......*.......................................................
........**.....................................................
.........*..*..................................................
**.............................................................
*.*...***......................................................
*...*....*.....................................................
...**..........................................................
...*.....*.....................................................
:anvil: The following {induction coil}.
.****.
*....*
.***.*
...*.**
:apgluxe: See {apgsearch}
:apgmera: See {apgsearch}.
:apgnano: See {apgsearch}.
:apgsearch: One of several versions of a client-side Ash Pattern
Generator {soup} search script by Adam P. Goucher, for use with
Conway's Life and a wide variety of other rules. Development of the
original {Golly}-based Python script started in August 2014. After
the addition in 2016 of apgnano (native C++) and apgmera
(self-modifying, 256-bit SIMD compatibility), development continues
in 2017 with apgluxe (Larger Than Life and Generations rules, more
soup shapes). Several customized variants of the Python script have
also been created by other programmers, to perform types of searches
not supported by Goucher's original apgsearch 1.x.
All of these versions of the search utility work with a "haul" that
usually consists of many thousands or millions of random soup
patterns. Each soup is run to stability and a detailed object census
results is reported to {Catagolue}. For any rare objects discovered
in the {ash}, the source soup can be easily retrieved from the
Catagolue server.
:APPS: (c/5 orthogonally, p30) An asymmetric {PPS}. The same as the
{SPPS}, but with the two halves 15 generations out of phase with one
another. Found by Alan Hensel in May 1998.
:ark: A pair of mutually stabilizing {switch engine}s. The archetype
is {Noah's ark}. The diagram below shows an ark found by Nick Gotts
that takes until generation 736692 to stabilize, and can therefore be
considered as a {methuselah}.
...........................*....
............................*...
.............................*..
............................*...
...........................*....
.............................***
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
**..............................
..*.............................
..*.............................
...****.........................
:arm: A long extension hanging off from the main body of a {spaceship}
or {puffer} perpendicular to the direction of travel. For a
alternate meaning see {construction arm}.
A lot of known spaceships have multiple arms. This is an artefact
of the search methods used to find such spaceships, rather than an
indication of what a "typical" spaceship might look like.
:armless: A method of generating {slow salvo}s across a wide range of
lanes without using a {construction arm} with a movable {elbow}.
Instead, streams of gliders on two fixed opposing {lane}s collide
with each other to produce clean 90-degree output gliders. Slowing
down one of the streams by 8N ticks will move the output lanes of the
gliders toward the source of that stream by N {full diagonal}s. This
construction method was used to create the supporting slow salvos in
the {half-baked knightship}s, and also in the {Parallel HBK gun}.
:ash: The {stable} or oscillating debris left by a random reaction.
Experiments show that for random {soup}s with moderate initial
densities (say 0.25 to 0.5) the resulting ash has a density of about
0.0287. (This is, of course, based on what happens in finite fields.
In infinite fields the situation may conceivably be different in the
long run because of the effect of certain initially very rare objects
such as {replicator}s.)
:aVerage: (p5) Found by Dave Buckingham, 1973. The average number of
live {rotor} cells is five (V), which is also the period.
...**........
....***......
..*....*.....
.*.****.*....
.*.*....*..*.
**.***..*.*.*
.*.*....*..*.
.*.****.*....
..*....*.....
....***......
...**........
:B: = {B-heptomino}
:B29: (c/4 diagonally, p4) The following {spaceship}, found by Hartmut
Holzwart in April 2004.
.......***.......
.......*.........
***......*.......
*......*.*.......
.*....**.****....
...****.*****.**.
....**.......**.*
:B-52 bomber: The following p104 {double-barrelled} {glider} {gun}. It
uses a {B-heptomino} and emits one glider every 52 generations. It
was found by Noam Elkies in March 1996, except that Elkies used
{blocker}s instead of {mold}s, the improvement being found by David
Bell later the same month.
.**....................................
.**.................*..................
...................*.*............*.*..
....................*............*.....
**.......**.......................*..*.
**.*.....**.......................*.*.*
...*.......................*.......*..*
...*.......................**.......**.
*..*.................**.....*..........
.**..................*.................
.....................***...............
....................................**.
....................................**.
.**....................................
*..*...................................
*.*.*................*.*....**.....**..
.*..*.................**....**.....**.*
.....*............*...*...............*
..*.*............*.*..................*
..................*................*..*
....................................**.
:B60: A {Herschel conduit} discovered by Michael Simkin in 2015 using
his search program, {CatForce}. It is one of two known {Blockic}
{elementary conduit}s. After 60 ticks, it produces a Herschel
rotated 180 degrees at (x,y) relative to the input. It can most
easily be connected to another B60 conduit, producing a closed loop,
the {Simkin glider gun}.
*...........**.....**
***.........**.....**
..*..................
..*............**....
...............**....
.....................
.....................
.....................
.....................
......*..............
......*.*............
......***............
........*............
:babbling brook: Any {oscillator} whose {rotor} consists of a string of
cells each of which is adjacent to exactly two other rotor cells,
except for the endpoints which are adjacent to only one other rotor
cell. Compare {muttering moat}. Examples include the {beacon}, the
{great on-off}, the {light bulb} and the {spark coil}. The following
less trivial example (by Dean Hickerson, August 1997) is the only one
known with more than four cells in its rotor. It is p4 and has a
6-cell rotor.
.......*........
.....***....**..
....*...**..*...
.*..*.**..*.*...
*.*.*....**..**.
.**..**....*.*.*
...*.*..**.*..*.
...*..**...*....
..**....***.....
........*.......
:backrake: Another term for a backwards {rake}. A p8 example by Jason
Summers is shown below. See {total aperiodic} for a p12 example.
.....***...........***.....
....*...*.........*...*....
...**....*.......*....**...
..*.*.**.**.....**.**.*.*..
.**.*....*.**.**.*....*.**.
*....*...*..*.*..*...*....*
............*.*............
**.......**.*.*.**.......**
............*.*............
......***.........***......
......*...*.........*......
......*.*....***...........
............*..*....**.....
...............*...........
...........*...*...........
...........*...*...........
...............*...........
............*.*............
:backward glider: A {glider} which moves at least partly in the
opposite direction to the {puffer}(s) or {spaceship}(s) under
consideration.
:baker: (c p4 fuse) A {fuse} by Keith McClelland.
..............**
.............*.*
............*...
...........*....
..........*.....
.........*......
........*.......
.......*........
......*.........
.....*..........
....*...........
...*............
***.............
.*..............
:baker's dozen: (p12) A {loaf} {hassle}d by two {block}s and two
{caterer}s. The original form (using p4 and p6 oscillators to do the
hassling) was found by Robert Wainwright in August 1989.
**.........**..........
****.*.....**..........
*.*..***...............
...........*...........
....**....*.*..........
....*.....*..*....*....
...........**....**....
.......................
...............***..*.*
..........**.....*.****
..........**.........**
:bakery: (p1) A common formation of two bi-loaves.
....**....
...*..*...
...*.*....
.**.*...*.
*..*...*.*
*.*...*..*
.*...*.**.
....*.*...
...*..*...
....**....
:banana spark: a three-bit {polyplet} spark used in {glider
construction}. It can be used to turn a glider 90 degrees:
..*....
*.*....
.**....
....**.
......*
:barberpole: Any p2 oscillator in the infinite sequence {bipole},
{tripole}, {quadpole}, {pentapole}, {hexapole}, {heptapole} ... (It
wasn't my idea to suddenly change from Latin to Greek.) This sequence
of oscillators was found by the MIT group in 1970. The term is also
used (usually in the form "barber pole") to describe other
{extensible} sections of oscillators or spaceships, especially those
(usually of period 2) in which all generations look alike except for
a translation and/or rotation/reflection.
:barberpole intersection: = {quad}
:barber's pole: = {barberpole}
:barge: (p1)
.*..
*.*.
.*.*
..*.
:basic shuttle: = {queen bee shuttle}
:beacon: (p2) The third most common {oscillator}. Found by Conway,
March 1970.
**..
*...
...*
..**
:beacon maker: (c p8 fuse)
..............**
.............*.*
............*...
...........*....
..........*.....
.........*......
........*.......
.......*........
......*.........
.....*..........
....*...........
...*............
***.............
..*.............
..*.............
:beehive: (p1) The second most common {still life}.
.**.
*..*
.**.
:beehive and dock: (p1)
...**.
..*..*
...**.
......
.****.
*....*
**..**
:beehive on big table: = {beehive and dock}
:beehive pusher: = {hivenudger}
:beehive wire: See {lightspeed telegraph}.
:beehive with tail: (p1)
.**...
*..*..
.**.*.
....*.
....**
:Bellman: a program for searching catalytic reactions, developed by
Mike Playle, which successfully found the {Snark}.
:belly spark: The spark of a {MWSS} or {HWSS} other than the {tail
spark}.
:bent keys: (p3) Found by Dean Hickerson, August 1989. See also {odd
keys} and {short keys}.
.*........*.
*.*......*.*
.*.**..**.*.
....*..*....
....*..*....
:BFx59H: One of the earliest and most remarkable {converter}s,
discovered by Dave Buckingham in July 1996. In 59 generations it
transforms a B-heptomino into a clean Herschel with very good
clearance, allowing easy connections to other conduits. It forms the
final stage of many of the known {composite conduit}s, including the
majority of the original sixteen {Herschel conduit}s. Here a {ghost
Herschel} marks the output location:
.**.....................
..*.....................
.*......................
.**.....................
........................
........................
........................
........................
........................
*...**...............*..
**..**...............*..
.**..................***
.*.....................*
*.......................
:B-heptomino: (stabilizes at time 148) This is a very common pattern.
It often arises with the cell at top left shifted one space to the
left, which does not affect the subsequent evolution. B-heptominoes
acquired particular importance in 1996 due to Dave Buckingham's work
on {B track}s - see in particular {My Experience with B-heptominos in
Oscillators}.
*.**
***.
.*..
:B-heptomino shuttle: = {twin bees shuttle}
:bi-block: (p1) The smallest {pseudo still life}.
**.**
**.**
:bi-boat: = {boat-tie}
:biclock: The following {pure glider generator} consisting of two
{clock}s.
..*....
**.....
..**...
.*...*.
...**..
.....**
....*..
:big beacon: = {figure-8}
:big fish: = {HWSS}
:big glider: (c/4 diagonally, p4) This was found by Dean Hickerson in
December 1989 and was the first known diagonal {spaceship} other than
the {glider}.
...***............
...*..***.........
....*.*...........
**.......*........
*.*....*..*.......
*........**.......
.**...............
.*..*.....*.**....
.*.........**.*...
...*.*......**..*.
....**.*....**...*
........*.......*.
.......****...*.*.
.......*.**...****
........*...**.*..
.............**...
.........*.***....
..........*..*....
:big S: (p1)
....**.
...*..*
...*.**
**.*...
*..*...
.**....
:big table: = {dock}
:billiard table configuration: Any {oscillator} in which the {rotor} is
enclosed within the {stator}. Examples include {airforce},
{cauldron}, {clock II}, {Hertz oscillator}, {negentropy}, {pinwheel},
{pressure cooker} and {scrubber}.
:bi-loaf: This term has been used in at least three different senses. A
bi-loaf can be half a {bakery}:
.*.....
*.*....
*..*...
.**.*..
...*.*.
...*..*
....**. or it can be the following much less common {still
life}:
..*....
.*.*...
*..*...
.**.**.
...*..*
...*.*.
....*.. or the following {pure glider generator}:
..*.
.*.*
*..*
.**.
*..*
*.*.
.*..
:bipole: (p2) The {barberpole} of length 2.
**...
*.*..
.....
..*.*
...**
:bi-pond: (p1)
.**....
*..*...
*..*...
.**.**.
...*..*
...*..*
....**.
:bi-ship: = {ship-tie}
:bit: A live {cell}.
:biting off more than they can chew: (p3) Found by Peter Raynham, July
1972.
*...........
***.........
...*........
..**........
...**.......
....**......
...*..*.....
...*..**....
....**.***..
........*.*.
..........*.
..........**
:Black&White: = {Immigration}
:blasting cap: The {pi-heptomino} (after the shape at generation 1). A
term used at MIT and still occasionally encountered.
:blinker: (p2) The smallest and most common {oscillator}. Found by
Conway, March 1970.
***
:blinker puffer: Any {puffer} whose output is {blinker}s. However, the
term is particularly used for p8 c/2 puffers. The first such blinker
puffer was found by Robert Wainwright in 1984, and was unexpectedly
simple:
...*.....
.*...*...
*........
*....*...
*****....
.........
.........
.........
.**......
**.***...
.****....
..**.....
.........
.....**..
...*....*
..*......
..*.....*
..******.
Since then many more blinker puffers have been found. The following
one was found by David Bell in 1992 when he was trying to extend an
{x66}:
.............***.
............*****
...........**.***
............**...
.................
.................
.........*.*.....
..*.....*..*.....
.*****...*.*.....
**...**.**.......
.*.......*.......
..**..*..*.......
..........*......
..**..*..*.......
.*.......*.......
**...**.**.......
.*****...*.*.....
..*.....*..*.....
.........*.*.....
.................
.................
............**...
...........**.***
............*****
.............***.
The importance of this larger blinker puffer (and others like it), is
that the engine which produces the blinker output is only p4. The
blinker row produced by the puffer can easily be ignited, and burns
cleanly with a speed of 2c/3. When the burning catches up to the
engine, it causes a {phase change} in the puffer. This fact allows
p8 blinker puffers to be used to construct rakes of all periods which
are large multiples of four.
:blinker pull: The following glider/blinker collision, which moves a
blinker (-1,3) toward the glider source:
***.
....
....
....
.***
.*..
..*.
:blinkers bit pole: (p2) Found by Robert Wainwright, June 1977.
.....**
***.*.*
.......
.*.*..*
*....*.
**...*.
:blinker ship: A {growing spaceship} in which the wick consists of a
line of {blinker}s. An example by Paul Schick based on his {Schick
engine} is shown below. Here the front part is p12 and moves at c/2,
while the back part is p26 and moves at 6c/13. Every 156 generations
13 blinkers are created and 12 are destroyed, so the wick becomes one
blinker longer.
..........****.............
..........*...*............
..........*................
.**........*..*............
**.**......................
.****...*..................
..**...*.**........*....***
......*...*........*....*.*
..**...*.**........*....***
.****...*..................
**.**......................
.**........*..*............
..........*................
..........*...*............
..........****.............
:block: (p1) The most common {still life}.
**
**
:blockade: (p1) A common formation of four blocks. The final form of
{lumps of muck}.
**.....................
**.....................
.......................
.......................
.**.................**.
.**.................**.
.......................
.......................
.....................**
.....................**
:block and dock: (p1)
...**.
...**.
......
.****.
*....*
**..**
:block and glider: (stabilizes at time 106)
**..
*.*.
..**
:blocker: (p8) Found by Robert Wainwright. See also {filter}.
......*.*.
.....*....
**..*....*
**.*..*.**
....**....
:Blockic: adjective for {constellation}s consisting entirely of
{block}s. It's possible to arrange blocks in a way that can be
{trigger}ed by a single glider to produce any {glider-constructible}
pattern. See {seed}.
:block on big table: = {block and dock}
:block on table: (p1)
..**
..**
....
****
*..*
:block pull: The following glider/block collision, which moves a block
(2,1) toward the glider source:
**.
**.
...
...
...
...
***
*..
.*.
:block pusher: A pattern emitting streams of {glider}s which can
repeatedly push a block further away. This can be used as part of a
{sliding block memory}.
The following pattern, in which three gliders push a block one cell
diagonally, is an example of how a block pusher works.
...................*.*
...................**.
....................*.
......................
......................
......................
...*..................
..*...................
..***.................
......................
......................
......................
......................
**...*................
**...*.*..............
.....**...............
A universal {construction elbow} recipe library is also likely
to contain one or more block-pushing reactions, since blocks are
commonly used as elbows.
:blom: (stabilizes at time 23314) The following {methuselah}, found by
Dean Hickerson in July 2002.
*..........*
.****......*
..**.......*
..........*.
........*.*.
:blonk: A {block} or a {blinker}. This term is mainly used in the
context of {sparse Life} and was coined by Rich Schroeppel in
September 1992.
:blonker: (p6) The following {oscillator}, found by Nicolay Beluchenko
in April 2004.
*..**....*..
**..*.**.*..
....*.*.....
.....**.....
.......*....
.......*...*
.........*.*
..........*.
:boat: (p1) The only 5-cell {still life}.
**.
*.*
.*.
:boat-bit: A binary digit represented by the presence of a {boat} next
to a {snake} (or other suitable object, such as an {aircraft
carrier}). The bit can be toggled by a {glider} travelling along a
certain path. A correctly timed glider on a crossing path can detect
whether the transition was from 1 to 0 (in which case the crossing
glider is deleted) or from 0 to 1 (in which case it passes unharmed).
Three gliders therefore suffice for a non-destructive read. The
mechanisms involved are shown in the diagram below. Here the bit is
shown in state 0. It is about to be set to 1 and then switched back
to 0 again. The first crossing glider will survive, but the second
will be destroyed.
......*..................
.......*.................
.....***.................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
................*........
..............*.*........
..........**...**........
...........**............
..........*..........*.**
.....................**.*
.........................
.........................
.........................
.........................
.........................
.*.......................
.**......................
*.*......................
In January 1997 David Bell found a method of reading the bit while
setting it to 0. A {MWSS} is fired at the boat-bit. If it is
already 0 (absent) then the MWSS passes unharmed, but if it is 1
(present) then the boat and the MWSS are destroyed and, with the help
of an {eater1}, converted into a glider which travels back along
exactly the same path that is used by the gliders that toggle the
boat-bit.
................................................*........
................................................***......
...................................................*.....
..................................................**.....
.........................................................
.........................................................
.........................................................
.........................................................
..*......................................................
*...*..............................................*.....
.....*..............................*****...........*....
*....*.............................*....*.........***....
.*****..................................*................
...................................*...*.................
.....................................*...................
.........................................................
.........................................................
.......................................................**
........................................................*
.......................................................*.
.......................................................**
There are many other equivalent methods based on alternate incoming
test {signal}s.
:boat maker: (c p4 fuse)
................**
...............*.*
..............*...
.............*....
............*.....
...........*......
..........*.......
.........*........
........*.........
.......*..........
......*...........
.....*............
*****.............
....*.............
....*.............
....*.............
....*.............
:boat on boat: = {boat-tie}
:boat-ship-tie: = {ship tie boat}
:boatstretcher: See {tubstretcher}.
:boat-tie: (p1) A 10-cell {still life} consisting of two {boat}s placed
tip-to-tip. The name is a pun on "bow tie".
.*....
*.*...
.**...
...**.
...*.*
....*.
:bobsled: = {switch engine channel}.
:boojum reflector: (p1) Dave Greene's name for the following 180-degree
{glider} {reflector} which he found in April 2001, winning $100
bounties offered by Alan Hensel and Dietrich Leithner. The name is
taken from Lewis Carroll's _The Hunting of the Snark_, referring to
the fact that a small 90-degree stable reflector was really what was
wanted. 180-degree reflectors are relatively undesirable and have
limited use in larger circuitry constructions.
The boojum reflector was the smallest and fastest known stable
reflector until the discovery of the {rectifier} in 2009 and the
{Snark} in 2013.
....*.*......**.............................
.....**......**.............................
.....*......................................
............................................
............................................
............................................
............................................
............................................
............................................
........................................*...
.......................................*.*..
.......................................*.*..
....................**................**.**.
....................**......................
......................................**.**.
..**..................................**.*..
.*.*.......................................*
.*........................................**
**..........................................
............................................
..................................**........
..................................**....**..
...........**...........................*.*.
..........*.*.............................*.
..........*...............................**
.........**.......................**........
..................................**........
............................................
............................................
.............................*..............
............................*.*.............
.............................*..............
:bookend: The following {induction coil}. It is generation 1 of
{century}.
..**
*..*
***.
:bookends: (p1)
**...**
*.*.*.*
..*.*..
.**.**.
:boss: (p4) Found by Dave Buckingham, 1972.
.....*.....
....*.*....
....*.*....
...**.**...
..*.....*..
.*.*.*.*.*.
.*.*...*.*.
**.*...*.**
*..*.*.*..*
..*.....*..
...**.**...
....*.*....
....*.*....
.....*.....
:bottle: (p8) Found by Achim Flammenkamp in August 1994. The name is a
back-formation from {ship in a bottle}.
....**......**....
...*..*....*..*...
...*.*......*.*...
.**..***..***..**.
*......*..*......*
*.**..........**.*
.*.*..........*.*.
...**........**...
..................
..................
...**........**...
.*.*..........*.*.
*.**..........**.*
*......*..*......*
.**..***..***..**.
...*.*......*.*...
...*..*....*..*...
....**......**....
:bounding box: The smallest rectangular array of cells that contains
the whole of a given pattern. For {oscillator}s and {gun}s this
usually is meant to include all {phase}s of the pattern, but
excludes, in the case of guns, the outgoing stream(s).
:bow tie: = {boat-tie}
:brain: (c/3 orthogonally, p3) Found by David Bell, May 1992.
.***.........***.
*.*.**.....**.*.*
*.*.*.......*.*.*
.*.**.**.**.**.*.
.....*.*.*.*.....
...*.*.*.*.*.*...
..**.*.*.*.*.**..
..***..*.*..***..
..**..*...*..**..
.*....**.**....*.
.*.............*.
:breeder: Any pattern whose {population} grows at a quadratic rate,
although it is usual to exclude {spacefiller}s. It is easy to see
that this is the fastest possible growth rate.
The term is also sometimes used to mean specifically the breeder
created by Bill Gosper's group at MIT, which was the first known
pattern exhibiting superlinear growth.
There are four common types of breeder, known as MMM, MMS, MSM and
SMM (where M=moving and S=stationary). Typically an MMM breeder is a
{rake} {puffer}, an MMS breeder is a puffer producing puffers which
produce stationary objects ({still life}s and/or {oscillator}s), an
MSM breeder is a {gun} puffer and an SMM breeder is a rake gun. There
are, however, less obvious variants of these types. Other less
common breeder categories (SSS, hybrid MSS/MSM, etc.) can be created
with some difficulty, based on {universal constructor} technology;
see {Pianola breeder}.
The original breeder was of type MSM (a p64 puffer puffing p30
glider guns). The known breeder with the smallest initial population
is the {metacatacryst}.
:bridge: A term used in naming certain {still life}s (and the {stator}
part of certain {oscillator}s). It indicates that the object
consists of two smaller objects joined edge to edge, as in {snake
bridge snake}.
:broken lines: A pattern constructed by Dean Hickerson in May 2005
which produces complex broken lines of gliders and blocks.
:broth: = {soup}
:BRx46B: A {Spartan} {elementary conduit} discovered by Michael Simkin
on 25 April 2016, one of the relatively few known conduits that can
move a {B-heptomino} input to a B-heptomino output without an
intervening {Herschel} stage.
...........**
..**.......**
..**.........
.............
.............
*..........*.
.*........*.*
.**.......*.*
**.........*.
*............
:BTC: = {billiard table configuration}
:B track: A {track} for {B-heptomino}es. A B-heptomino becomes a
{Herschel} plus a {block} in twenty generations, so this term was
nearly synonymous with {Herschel track} until the discovery of
{elementary conduit}s that convert a B directly to another B, or to
some other non-Herschel signal output. See for example {BRx46B}.
:buckaroo: A {queen bee shuttle} stabilized at one end by an eater in
such a way that it can turn a glider, as shown below. This was found
by Dave Buckingham in the 1970s. The name is due to Bill Gosper.
..*.....................
*.*.....................
.**.....................
...........*............
.........*.*............
........*.*.............
.......*..*...........**
........*.*...........**
...**....*.*............
..*.*......*............
..*.....................
.**.....................
:bullet heptomino: Generation 1 of the {T-tetromino}.
.*.
***
***
:bun: The following {induction coil}. By itself this is a common
{predecessor} of the {honey farm}. See also {cis-mirrored R-bee}.
.**.
*..*
.***
:bunnies: (stabilizes at time 17332) This is a {parent} of {rabbits}
and was found independently by Robert Wainwright and Andrew
Trevorrow.
*.....*.
..*...*.
..*..*.*
.*.*....
:burloaf: = {loaf}
:burloaferimeter: (p7) Found by Dave Buckingham in 1972. See also
{airforce}.
....**....
.....*....
....*.....
...*.***..
...*.*..*.
**.*...*.*
**.*....*.
....****..
..........
....**....
....**....
:bushing: That part of the {stator} of an {oscillator} which is
adjacent to the {rotor}. Compare {casing}.
:butterfly: The following pattern, or the formation of two beehives
that it evolves into after 33 generations. (Compare {teardrop},
where the beehives are five cells closer together.)
*...
**..
*.*.
.***
:Bx125: An {elementary conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Paul Callahan in November 1998. After 125
ticks, it produces an inverted {Herschel} rotated 180 degrees at (-9,
-17) relative to the input. Its {recovery time} is 166 ticks. A
{ghost Herschel} in the pattern below marks the output location:
...........................*..........
..*.......................*.*.........
..*.......................*.*.........
***.........**...........**.***.......
*...........**.................*......
.........................**.***.......
.........................**.*.........
......................................
......................................
......................................
......................................
......................................
......................................
......................................
......................................
....................................**
....................................**
......................................
.........*............................
.........*.*..........................
.........***..........................
...........*..........................
......................................
.......................**.............
.......................*..............
........................***...........
..........................*...........
:Bx222: A {composite conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Paul Callahan in October 1998. It is made
up of three {elementary conduit}s, HF95P + PB68B + {BFx59H}. After
222 ticks, it produces a backward-traveling inverted {Herschel} at
(6, -16) relative to the input. Its {recovery time} is 271 ticks. A
{ghost Herschel} in the pattern below marks the output location:
.............*............................
....**.....***.......**...................
.....*....*..........*....................
.....*.*...*..........*...................
......*.*...*........**...................
.......*...**.................*......*....
............................***.....*.*...
...........................*........*.*...
...........................**......**.***.
.........................................*
..*...............**...............**.***.
..*...............**...............**.*...
***.......................................
*.........................................
..........................................
..........................................
........................................**
........................................*.
......................................*.*.
......................................**..
..........................................
..........................................
..........................................
..........................................
..........................................
..........................................
......*...................................
......*.*.................................
......***.................................
........*....................**...........
.............................*............
..................**..........*...........
..................**..**.....**...........
......................*.*.................
........................*.................
........................**................
:by flops: (p2) Found by Robert Wainwright.
...*..
.*.*..
.....*
*****.
.....*
.*.*..
...*..
:c: = {speed of light}
:c/10 spaceship: A {spaceship} travelling at one tenth of the {speed of
light}. The first such spaceship to be discovered was the
orthogonally traveling {copperhead}, found by 'zdr' on 5 March 2016.
Simon Ekstrom found the related {fireship} two weeks later. A
{Caterloopillar} can theoretically be configured to move at c/10, but
there are technical difficulties with speeds of the form 4x+2, and as
of August 2017 this has not been done in practice.
:c/12 spaceship: A {spaceship} travelling at one twelfth of the {speed
of light}. The only diagonal spaceships that are currently known to
move at this speed are the {Cordership}s. An orthogonal
{Caterloopillar} spaceship has been configured to move at c/12.
:c/2 spaceship: A {spaceship} travelling at half the {speed of light}.
Such spaceships necessarily move orthogonally. The first to be
discovered was the {LWSS}. For other examples see {Coe ship},
{ecologist}, {flotilla}, {hammerhead}, {hivenudger}, {HWSS}, {MWSS},
{puffer train}, {puff suppressor}, {pushalong}, {Schick engine},
{sidecar}, {still life tagalong} and {x66}.
:c/3 spaceship: A {spaceship} travelling at one third of the {speed of
light}. All known c/3 spaceships travel orthogonally, and the first
was found in August 1989 by Dean Hickerson. For further examples see
{brain}, {dart}, {edge-repair spaceship}, {fly}, {turtle} and {wasp}.
A spaceship moving diagonally at an angle of 45 degree cannot travel
at a speed of c/3, but it is likely that c/3 {knightship}s exist,
though none have yet been found.
:c/4 spaceship: A {spaceship} travelling at one quarter of the {speed
of light}. The first such spaceship to be discovered was, of course,
the {glider}, and this remained the only known example until December
1989, when Dean Hickerson found the first orthogonal example,
{119P4H1V0}, and also a new diagonal example (the {big glider}). For
other examples see {B29}, {Canada goose}, {crane}, {Enterprise},
{edge-repair spaceship} (third pattern), {non-monotonic}, {Orion},
{quarter}, {sparky}, {swan} and {tagalong}. It is known that c/4 is
the fastest possible speed for a (45-degree) diagonal spaceship.
:c/5 spaceship: A {spaceship} travelling at one fifth of the {speed of
light}. The first such spaceship to be discovered was the {snail},
found by Tim Coe in January 1996. The first diagonally moving
example, {295P5H1V1}, was found by Jason Summers in November 2000.
In January 2005, Summers found the smaller diagonal specimen shown
below.
..........**..........
.........*..*.........
........**............
.........*.**.........
..........*.***.......
..........**.***......
............*....**...
............***....**.
..*.........*.*.......
.***........*..*......
*...**................
*..*.*.......**.*..*..
.*.**.****...*...****.
....**.*...**.......*.
....**.**..*.........*
.....*...*........*.**
...........*.......*..
......*.....*......*..
......*.....*..*......
.......*...**...**....
.......*....**.*......
..............**......
A {Caterloopillar} has also been configured to move at c/5.
:c/6 spaceship: A {spaceship} travelling at one sixth of the {speed of
light}. The first such spaceship to be discovered was the {dragon},
found by Paul Tooke in April 2000. The first diagonally moving
example was the {seal}, found by Nicolay Beluchenko in September
2005. Another orthogonal c/6 spaceship, found by Paul Tooke in March
2006, is shown below.
..*..............*..................................*.....
*..*..***.......*.****...............**...........**.*....
*..*............***.*.*.........*.....*.......*...*.......
.*.*..*.....................***..*.*.***.....*.*.*....*...
..**......*....*................******..*..*...*...*..*...
.*.*...**.....*...**......**.**..*..**..*.*.**..*.........
..*.....*.**..*...**......**....*.*.*..*..*.*.*......**..*
..*....***..*.........***.......***.*.**.....*.......***.*
............*********...*........**.***...****.........*.*
..........................................................
............*********...*........**.***...****.........*.*
..*....***..*.........***.......***.*.**.....*.......***.*
..*.....*.**..*...**......**....*.*.*..*..*.*.*......**..*
.*.*...**.....*...**......**.**..*..**..*.*.**..*.........
..**......*....*................******..*..*...*...*..*...
.*.*..*.....................***..*.*.***.....*.*.*....*...
*..*............***.*.*.........*.....*.......*...*.......
*..*..***.......*.****...............**...........**.*....
..*..............*..................................*.....
A {Caterloopillar} can theoretically be configured to move at c/10,
but there are technical difficulties with speeds of the form 4x+2,
and as of August 2017 this has not been done in practice.
:c/7 spaceship: A {spaceship} travelling at one seventh of the {speed
of light}. The first such spaceship to be discovered was the
diagonally traveling {lobster}, found by Matthias Merzenich in August
2011. The first known orthogonal c/7 spaceship was the {loafer},
discovered by Josh Ball in February 2013. A {Caterloopillar} has
been configured to move at c/7.
:CA: = {cellular automaton}
:caber tosser: Any pattern whose {population} is asymptotic to c.log(t)
for some constant c, and which contains a {glider} (or other
{spaceship}) bouncing between a slower receding spaceship and a fixed
{reflector} which emits a spaceship (in addition to the reflected
one) whenever the bouncing spaceship hits it.
As the receding spaceship gets further away the bouncing spaceship
takes longer to complete each cycle, and so the extra spaceships
emitted by the reflector are produced at increasingly large
intervals. More precisely, if v is the speed of the bouncing
spaceship and u the speed of the receding spaceship, then each
interval is (v+u)/(v-u) times as long as the previous one. The
population at time t is therefore n.log(t)/log((v+u)/(v-u)) + O(1),
where n is the population of one of the extra spaceships (assumed
constant).
The first caber tosser was built by Dean Hickerson in May 1991.
:Callahan G-to-H: A stable {glider reflector} and glider-to-Herschel
{converter} discovered by Paul Callahan in November 1998. Its
recovery time is 575 ticks. The initial stage converts two gliders
into a Herschel. A {ghost Herschel} in the pattern below marks the
output location:
....*.........*...................
....***.....***...................
.*.....*...*......................
..*...**...**.....................
***...............................
.........*........................
........*.*.......................
........*.*.......................
.........*........................
...............................*..
...............................*..
....................**.........***
..............**....**...........*
........**...**...................
.......*..*....*..................
..**....**........................
.*.*..............................
.*................................
**................................
..........**......................
..........*.......................
...........***....................
.............*....................
The glider from the southeast can be supplied by a {Fx77} + {L112}
+ Fx77 Herschel track, or by reflecting the output Herschel's {FNG}
as in the {p8 G-to-H}. See also {Silver reflector}, {Silver G-to-H}.
:Cambridge pulsar CP 48-56-72: = {pulsar} (The numbers refer to the
populations of the three {phase}s. The Life pulsar was indeed
discovered at Cambridge, like the first real pulsar a few years
earlier.)
:Canada goose: (c/4 diagonally, p4) Found by Jason Summers, January
1999. It consists of a {glider} plus a {tagalong}.
***..........
*.........**.
.*......***.*
...**..**....
....*........
........*....
....**...*...
...*.*.**....
...*.*..*.**.
..*....**....
..**.........
..**.........
At the time of its discovery the Canada goose was the smallest known
diagonal {spaceship} other than the glider, but this record has since
been beaten, first by the second spaceship shown under {Orion}, and
more recently by {quarter}.
:candelabra: (p3) By Charles Trawick. See also the note under {cap}.
....**....**....
.*..*......*..*.
*.*.*......*.*.*
.*..*.****.*..*.
....*.*..*.*....
.....*....*.....
:candlefrobra: (p3) Found by Robert Wainwright in November 1984.
.....*....
.*.**.*.**
*.*...*.**
.*....*...
.....**...
The following diagram shows that a pair of these can act in some ways
like {killer toads}. See also {snacker}.
....*...........*....
**.*.**.*...*.**.*.**
**.*...*.*.*.*...*.**
...*....*...*....*...
...**...........**...
.....................
.....................
.........***.........
.........*..*........
.........*...........
.........*...*.......
.........*...*.......
.........*...........
..........*.*........
:canoe: (p1)
...**
....*
...*.
*.*..
**...
:cap: The following {induction coil}. It can also be easily be
stabilized to form a p3 oscillator - see {candelabra} for a slight
variation on this.
.**.
*..*
****
:carnival shuttle: (p12) Found by Robert Wainwright in September 1984
(using {MW emulator}s at the end, instead of the {monogram}s shown
here).
.................................*...*
**...**..........................*****
.*.*.*...*..*......**...*..*.......*..
.**.**..**...**....**..**...**....*.*.
.*.*.*...*..*......**...*..*.......*..
**...**..........................*****
.................................*...*
:carrier: = {aircraft carrier}
:casing: That part of the {stator} of an {oscillator} which is not
adjacent to the {rotor}. Compare {bushing}.
:catacryst: A 58-cell quadratic growth pattern found by Nick Gotts in
April 2000. This was formerly the smallest known pattern with
superlinear growth, but has since been superseded by the related
{metacatacryst}, and later by {Gotts dots}, {wedge}, {26-cell
quadratic growth}, {25-cell quadratic growth}, {24-cell quadratic
growth}, and {switch-engine ping-pong}.
The catacryst consists of three {ark}s plus a glider-producing
{switch engine}. It produces a block-laying switch engine every
47616 generations. Each block-laying switch engine has only a finite
life, but the length of this life increases linearly with each new
switch engine, so that the pattern overall grows quadratically, as an
unusual type of MMS {breeder}.
:Catagolue: An online database of objects in Conway's Game of Life and
similar cellular automata, set up by Adam P. Goucher in 2015 at
{http://catagolue.appspot.com}. It gathers data from a distributed
search of random initial configurations and records the eventual
decay products. Within a year of operation it had completed a census
of the {ash} objects from over two trillion asymmetric 16x16 soups.
As of August 2017 the number is near ten trillion.
It is often possible to find equivalent {glider synthesis} recipes
for selected parts of long-running active reactions. Results from
these random {soup} searches have made it possible to find efficient
construction methods for thousands of increasingly rare {still life}s
and {oscillator}s, and the occasional {puffer} or {spaceship}. In
many of these cases a {glider synthesis} was previously very
difficult or unknown.
:catalyst: An object that participates in a reaction but emerges from
it unharmed. The term is mostly applied to {still life}s, but can
also be used of {oscillator}s, {spaceship}s, etc. The still lifes
and oscillators which form a {conduit} are examples of catalysts.
:caterer: (p3) Found by Dean Hickerson, August 1989. Compare with
{jam}. In terms of its minimum {population} of 12 this is the
smallest p3 {oscillator}. See also {double caterer} and {triple
caterer}.
..*.....
*...****
*...*...
*.......
...*....
.**.....
More generally, any oscillator which serves up a {bit} in the same
manner may be referred to as a caterer.
:Caterloopillar: A family of adjustable-speed spaceships constructed by
Michael Simkin in 2016, based on idea originally proposed by David
Bell. The front and back halves of Caterloopillars each function as
universal constructors, with each half constructing the building
blocks of the other half, while also reading and moving a
construction tape. The overall design is reminiscent of M.C. Escher's
lithograph "Drawing Hands". The name "Caterloopillar" is a reference
to Douglas Hofstader's Strange Loop concept.
Simkin has written an automated script that can construct a
Caterloopillar for any rational speed strictly less than c/4 -- with
some exceptions, mostly having to do with the size of the resulting
spaceship. Lower speeds in general require larger constructions, and
for any given computer system it is easy to choose a speed so slow
that it is impractical to construct a Caterloopillar for it..
As of August 2017 one significant remaining limitation is that
Caterloopillars with periods c/(6+4N) can't be constructed. However,
this is only a limitation of the current construction script, not of
the underlying Caterloopillar {universal toolkit}.
:Caterpillar: A {spaceship} that works by laying tracks at its front
end. The only example constructed to date is a p270 17c/45 spaceship
built by Gabriel Nivasch in December 2004, based on work by himself,
Jason Summers and David Bell. This Caterpillar has a population of
about 12 million in each generation and was put together by a
computer program that Nivasch wrote. At the time it was by far the
largest and most complex Life object ever constructed, and it is
still one of the largest in terms of population.
The 17c/45 Caterpillar is based on the following reaction between a
{pi-heptomino} and a {blinker}:
...............*
*.............**
*............**.
*.............**
...............*
In this reaction, the pi moves forward 17 cells in the course of 45
generations, while the blinker moves back 6 cells and is rephased.
This reaction has been known for many years, but it was only in
September 2002 that David Bell suggested that it could be used to
build a 17c/45 spaceship, based on a reaction he had found in which
pis crawling along two rows of blinkers interact to emit a glider
every 45 generations. Similar glider-emitting interactions were
later found by Gabriel Nivasch and Jason Summers. The basic idea of
the spaceship design is that streams of gliders created in this way
can be used to construct fleets of {standard spaceship}s which convey
gliders to the front of the blinker tracks, where they can be used to
build more blinkers.
A different Caterpillar may be possible based on the following
reaction, in which the pattern at top left reappears after 31
generations displaced by (13,1), having produced a new NW-travelling
glider. In this case the tracks would be waves of backward-moving
gliders.
.**.....................
...*....................
...*.**.................
***....*................
.......*................
.....***................
........................
........................
........................
........................
........................
........................
.....................***
.....................*..
......................*.
For other Caterpillar-type constructions see {Centipede}, {waterbear},
{half-baked knightship}, and {Caterloopillar}.
:CatForce: An optimized search program written by Michael Simkin in
2015, using brute-force enumeration of small {Spartan} objects in a
limited area, instead of a depth-first tree search. One major
purpose of CatForce is to find glider-constructible completions for
signal conduits. An early CatForce discovery was the {B60} conduit,
which enabled a record-breaking new glider gun.
:Catherine wheel: = {pinwheel}
:cauldron: (p8) Found in 1971 independently by Don Woods and Robert
Wainwright. Compare with {Hertz oscillator}.
.....*.....
....*.*....
.....*.....
...........
...*****...
*.*.....*.*
**.*...*.**
...*...*...
...*...*...
....***....
...........
....**.*...
....*.**...
:cavity: = {eater plug}
:cell: The fundamental unit of space in the Life universe. The term is
often used to mean a live cell - the sense is usually clear from the
context.
:cellular automaton: A certain class of mathematical objects of which
{Life} is an example. A cellular automaton consists of a number of
things. First there is a positive integer n which is the dimension
of the cellular automaton. Then there is a finite set of states S,
with at least two members. A state for the whole cellular automaton
is obtained by assigning an element of S to each point of the
n-dimensional lattice Z^n (where Z is the set of all integers). The
points of Z^n are usually called cells. The cellular automaton also
has the concept of a neighbourhood. The neighbourhood N of the
origin is some finite (nonempty) subset of Z^n. The neighbourhood of
any other cell is obtained in the obvious way by translating that of
the origin. Finally there is a transition rule, which is a function
from S^N to S (that is to say, for each possible state of the
neighbourhood the transition rule specifies some cell state). The
state of the cellular automaton evolves in discrete time, with the
state of each cell at time t+1 being determined by the state of its
neighbourhood at time t, in accordance with the transition rule.
There are some variations on the above definition. It is common to
require that there be a quiescent state, that is, a state such that
if the whole universe is in that state at generation 0 then it will
remain so in generation 1. (In Life the OFF state is quiescent, but
the ON state is not.) Other variations allow spaces other than Z^n,
neighbourhoods that vary over space and/or time, probabilistic or
other non-deterministic transition rules, etc.
It is common for the neighbourhood of a cell to be the 3x...x3
(hyper)cube centred on that cell. (This includes those cases where
the neighbourhood might more naturally be thought of as a proper
subset of this cube.) This is known as the Moore neighbourhood.
:centinal: (p100) Found by Bill Gosper. This combines the mechanisms
of the p46 and p54 shuttles (see {twin bees shuttle} and {p54
shuttle}).
**................................................**
.*................................................*.
.*.*.....................**.....................*.*.
..**........*............**............**.......**..
...........**..........................*.*..........
..........**.............................*..........
...........**..**......................***..........
....................................................
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...........**..**......................***..........
..........**.............................*..........
...........**..........................*.*..........
..**........*............**............**.......**..
.*.*.....................**.....................*.*.
.*................................................*.
**................................................**
:Centipede: (31c/240 orthogonally, p240) The smallest known {31c/240}
spaceship, constructed by Chris Cain in September 2014 as a
refinement of the {shield bug}.
:century: (stabilizes at time 103) This is a common pattern which
evolves into three {block}s and a {blinker}. In June 1996 Dave
Buckingham built a neat p246 glider {gun} using a century as the
engine. See also {bookend} and {diuresis}.
..**
***.
.*..
:channel: A lane or {signal} path, usually synchronized with one or
more coordinated signals on other paths. See {Gemini}, {Geminoid},
{construction arm}, {single-channel}.
:chemist: (p5)
.......*.......
.......***.....
..........*....
.....***..*..**
....*.*.*.*.*.*
....*...*.*.*..
.**.*.....*.**.
..*.*.*...*....
*.*.*.*.*.*....
**..*..***.....
....*..........
.....***.......
.......*.......
:C-heptomino: Name given by Conway to the following {heptomino}, a less
common variant of the {B-heptomino}.
.***
***.
.*..
:Cheshire cat: A block {predecessor} by C. R. Tompkins that
unaccountably appeared both in Scientific American and in {Winning
Ways}. See also {grin}.
.*..*.
.****.
*....*
*.**.*
*....*
.****.
:chicken wire: A type of {stable} {agar} of {density} 1/2. The
simplest version is formed from the tile:
**..
..**
But the "wires" can have length greater than two and need not all be
the same. For example:
**...****.....
..***....*****
:chirality: A term borrowed from chemistry to describe asymmetrical
patterns with two distinct mirror-image orientations. One common use
is in relation to {Herschel transmitter}s, where the spacing between
the two gliders in the {tandem glider} output can limit the
{receiver} to a single chirality.
:cigar: = {mango}
:circuit: Any combination of {conduit}s or {converter}s that moves or
processes an active signal. This includes components with multiple
states such as {period multiplier}s or {switch}es, which can be used
to build {gun}s, logic gates, {universal constructor}s, and other
computation or construction circuitry.
:cis-beacon on anvil: (p2)
...**.
....*.
.*....
.**...
......
.****.
*....*
.***.*
...*.**
:cis-beacon on table: (p2)
..**
...*
*...
**..
....
****
*..*
:cis-boat with tail: (p1)
.*...
*.*..
**.*.
...*.
...**
:cis fuse with two tails: (p1) See also {pulsar quadrant}.
...*..
.***..
*...**
.*..*.
..*.*.
...*..
:cis-mirrored R-bee: (p1)
.**.**.
*.*.*.*
*.*.*.*
.*...*.
:cis snake: = {canoe}
:clean: Opposite of {dirty}. A reaction which produces a small number
of different products which are desired or which are easily deleted
is said to be clean. For example, a {puffer} which produces just one
object per period is clean. Clean reactions are useful because they
can be used as building blocks in larger constructions.
When a {fuse} is said to be clean, or to burn cleanly, this usually
means that no debris at all is left behind.
:clearance: In signal circuitry, the distance from an {edge shooter}
output lane to the last unobstructed lane adjacent to the
edge-shooter circuitry. For example, an {Fx119 inserter} has an
unusually high 27{hd} clearance:
:clock: (p2) Found by Simon Norton, May 1970. This is the fifth or
sixth most common {oscillator}, being about as frequent as the
{pentadecathlon}, but much less frequent than the {blinker}, {toad},
{beacon} or {pulsar}. But it's surprisingly rare considering its
small size.
..*.
*.*.
.*.*
.*..
:clock II: (p4) Compare with {pinwheel}.
......**....
......**....
............
....****....
**.*....*...
**.*..*.*...
...*..*.*.**
...*.*..*.**
....****....
............
....**......
....**......
:clock inserter: = {clock insertion}.
:clock insertion: A uniquely effective method of adding a glider to the
front edge of a {salvo}, by first constructing a {clock}, then
converting it to a glider using a one-bit {spark}. Here it rebuilds
a sabotaged eater in a deep pocket between other gliders:
..................................................*........
..................................................*.*......
..................................................**.......
...............................................*......*....
..............................................*......*.....
..............................................***....***...
...........................................................
...........................................*......*........
...........................................*.*....*.*.....*
...........................................**.....**....**.
........................................*.......*........**
.......................................*...................
.......................................***...........*.*...
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*..................................................*.......
.**..............................................**........
**................................................**.......
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In 2015 Chris Cain used this reaction to demonstrate conclusively
that any unidirectional glider {salvo}, no matter how large or
tightly packed, can be constructed by collisions between gliders that
are initially separated by any finite distance. As a corollary,
because all glider syntheses are made up of two to four
unidirectional salvos, any glider-constructible object has a
synthesis that starts with every glider at least N cells away from
every other glider (for any chosen N).
:cloud of smoke: = {smoke}
:cloverleaf: This name was given by Robert Wainwright to his p2
oscillator {washing machine}. But Achim Flammenkamp also gave this
name to {Achim's p4}.
:cluster: Any pattern in which each live cell is connected to every
other live cell by a path that does not pass through two consecutive
dead cells. This sense is due to Nick Gotts, but the term has also
been used in other senses, often imprecise.
:CNWH: Conweh, creator of the Life universe.
:Coe ship: (c/2 orthogonally, p16) A {puffer engine} discovered by Tim
Coe in October 1995.
....******
..**.....*
**.*.....*
....*...*.
......*...
......**..
.....****.
.....**.**
.......**.
In December 2015, the Coe ship was discovered in an asymmetric
random {soup} on {Catagolue}. This was the first time any non-p4 ship
was discovered in a random asymmetric soup experiment, winning Adam
Goucher a 50-euro prize offered by Ivan Fomichev.
:Coe's p8: (p8) Found by Tim Coe in August 1997.
**..........
**..**......
.....**.....
....*..*....
.......*..**
.....*.*..**
:colour-changing: See {colour of a glider}. The period-8 reflector
shown in {reflector} is colour-changing, as are its p4/5/6/7 and
higher-period versions.
:colourised Life: A {cellular automaton} which is the same as Life
except for the use of a number of different ON states ("colours").
All ON states behave the same for the purpose of applying the Life
rule, but additional rules are used to specify the colour of the
resulting ON cells. Examples are {Immigration} and {QuadLife}.
:colour of a glider: The colour of a {glider} is a property of the
glider which remains constant while the glider is moving along a
straight path, but which can be changed when the glider bounces off a
{reflector}. It is an important consideration when building
something using reflectors.
The colour of a glider can be defined as follows. First choose
some cell to be the origin. This cell is then considered to be
white, and all other cells to be black or white in a checkerboard
pattern. (So the cell with coordinates (m,n) is white if m+n is
even, and black otherwise.) Then the colour of a glider is the
colour of its leading cell when it is in a phase which can be rotated
to look like this:
***
..*
.*.
A reflector which does not change the colour of gliders obviously
cannot be used to move a glider onto a path of different colour than
it started on. But a 90-degree reflector which does change the
colour of gliders is similarly limited, as the colour of the
resulting glider will depend only on the direction of the glider, no
matter how many reflectors are used. For maximum flexibility,
therefore, both types of reflector are required.
:colour-preserving: See {colour of a glider}. A {Snark} is a
colour-preserving reflector.
:complementary blinker: = {fore and back}
:component: A partial {glider synthesis} that can be used in the same
way in multiple {glider recipe}s. A component transforms part of an
object under construction in a well-defined way, without affecting
the rest of the object. For example, this well-known component can
be used to add a {hook} to any object that includes a protruding
{table} end, converting it to a {long bookend}:
.......*...................*...................*
.....**..................**..................**.
......**..................**..................**
................................................
..*...................*...................*.....
*.*.................*.*.................*.*.....
.**..*...............**..*...............**..*..
.....*.*.................*.*.................*.*
.....**..................**..................**.
................................................
................................................
....................*...........................
...*..*............*.*.*..*............**..*..*.
...****.............**.****............*...****.
......................*.................***.....
.....**...............*.*.................*.*...
.....**................*.*.................**...
........................*.......................
:composite: = {composite conduit}.
:composite conduit: A signal-processing {conduit} that can be
subdivided into two or more {elementary conduit}s.
:compression: = {repeat time}, {recovery time}.
:computational universality: See {universal computer}.
:conduit: Any arrangement of {still life}s and/or {oscillator}s which
move an active object to another location, perhaps also transforming
it into a different active object at the same time, but without
leaving any permanent debris (except perhaps gliders, or other
spaceships) and without any of the still lifes or oscillators being
permanently damaged. Probably the most important conduit is the
following remarkable one (Dave Buckingham, July 1996) in which a
{B-heptomino} is transformed into a {Herschel} in 59 generations.
.........**.*
*.**......***
**.*.......*.
.............
.........**..
.........**..
Several hundred {elementary conduit}s are now known, with recent
discoveries primarily made via search programs such as {CatForce} and
{Bellman}.
:conduit 1: {BFx59H}.
:confused eaters: (p4) Found by Dave Buckingham before 1973.
*..........
***........
...*.......
..*........
..*..*.....
.....*.....
...*.*.....
...**..**..
.......*.*.
.........*.
.........**
:constellation: A general term for a group of two or more separate
objects, usually small still lifes and low-period oscillators.
Compare {pseudo still life}.
:construction arm: An adjustable mechanism in a {universal constructor}
that allows new objects to be constructed in any chosen location that
the arm can reach. A construction arm generally consists of a
{shoulder} containing fixed guns or edge shooters, a movable
{construction elbow} that slides forward and backward along the
{construction lane}(s), and in the case of {single-arm} universal
constructors, a {hand} target object at the construction site that
can be progressively modified by a {slow salvo} to produce each
desired object.
:construction elbow: One of the components of a {construction arm} in a
{universal constructor}. The elbow usually consists of a single
{Spartan} still life or small constellation. It accepts {elbow
operation} recipes, in the form of {salvo}s coming from the
construction arm's {shoulder}.
These recipes may do one of several things: 1) {pull} the elbow
closer to the shoulder, 2) {push} the elbow farther from the
shoulder, 3) emit a glider on a particular output {lane} (while also
optionally pushing or pulling the elbow); 4) create a "{hand}" target
block or other useful object as a target for output gliders, to one
side of the {construction lane}; 5) duplicate the elbow, or 6)
destroy the elbow.
Elbows that receive and emit orthogonally-traveling {spaceship}s
instead of gliders are technically possible, but no working examples
are currently known. The discussion below assumes that gliders are
used to communicate between the shoulder, elbow, and hand locations.
If a mechanism can be programmed to generate recipes for at least
the first three options listed above, it is generally capable of
functioning as a {universal constructor}. The main requirement is
that push and pull {elbow operation}s should be available that are
either minimal (1{fd}) or the distances should be relatively prime.
Depending on the {elbow operation} library, there may be only one
type of elbow, or there may be two or more elbow objects, with
recipes that convert between them. The {9hd} library had just one
elbow type, a block. The original {10hd} library had two elbows,
blocks in mirror-symmetric locations; this was expanded to a larger
list for the {10hd Demonoid}. The {0hd Demonoid} also has a
multi-elbow recipe library. A {slow elbow} toolkit may make use of
an even larger number of glider output recipes, because the {target}
elbow object in that case is not restricted to a single diagonal
line.
If only one color, parity, or phase of glider can be emitted, then
the mechanism will be limited to producing {monochromatic salvo}s or
{monoparity salvo}s. These are less efficient at most construction
tasks, but are still generally accepted to enable {universal
toolkit}s. See also {half-baked knightship}.
:construction envelope: the region affected by an active reaction, such
as a {glider construction} of an object. The envelope corresponds to
the state-2 blue cells in {LifeHistory}. See also {edgy}.
:construction lane: Part of a {construction arm} between the {shoulder}
and the {elbow} -- in particular, one of the fixed {lane}s that
{elbow operation} signals travel on. All known {universal
constructor}s have used arms with two or more construction lanes,
except for the {0hd Demonoid} and {single-lane} construction recipes.
:construction universality: See {universal constructor}.
:converter: A {conduit} in which the input object is not of the same
type as the output object. This term tends to be preferred when
either the input object or the output object is a {spaceship}.
The following diagram shows a p8 {pi-heptomino}-to-{HWSS}
converter. This was originally found by Dave Buckingham in a larger
form (using a {figure-8} instead of the {boat}). The improvement
shown here is by Bill Gosper (August 1996). Dieter Leithner has
since found (much larger) {oscillator}s of periods 44, 46 and 60 that
can be used instead of the {Kok's galaxy}.
.*.*..*........
.***.*.**......
*......*.....*.
.*.....**...*.*
.............**
**.....*.......
.*......*......
**.*.***.......
..*..*.*.......
............***
............*.*
............*.*
Other {elementary conduit} converters include {BFx59H}, {135-degree
MWSS-to-G}, and {45-degree MWSS-to-G}.
:convoy: A collection of {spaceship}s all moving in the same direction
at the same speed.
:copperhead: (c/10 orthogonally, p10) The following small c/10
{spaceship}, discovered by conwaylife.com forum user 'zdc' on 5 March
2016, using a simple depth-first search program. A {glider
synthesis} was found on the same day.
.****.
......
.*..*.
*.**.*
*....*
......
*....*
**..**
******
.*..*.
..**..
..**..
Later that same month Simon Ekstrom added a {sparky} {tagalong} for
the copperhead to produce the {fireship}. This allowed for the
construction of c/10 puffers and rakes.
:Corder-: Prefix used for things involving {switch engine}s, after
Charles Corderman.
:Corder engine: = {switch engine}
:Cordergun: A {gun} firing {Cordership}s. The first was built by Jason
Summers in July 1999, using a {glider synthesis} by Stephen Silver.
:Cordership: Any {spaceship} based on {switch engine}s. These
necessarily move at a speed of c/12 diagonally with a period of 96
(or a multiple thereof). The first was found by Dean Hickerson in
April 1991. Corderships are the slowest spaceships so far
constructed, although arbitrarily slow spaceships are known to exist
(see {universal constructor}). Hickerson's original Cordership used
13 switch engines. He soon reduced this to 10, and in August 1993 to
7. In July 1998 he reduced it to 6. In January 2004, Paul Tooke
found the 3-engine Cordership shown below.
................................**.*...........................
...............................***.*......*.*..................
..............................*....*.*....*....................
...............................**......*.*...*.................
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........................**...**.*****..........................
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..**.*.........................................................
.***.*......*.*................................................
*....*.*....*..................................................
.**......*.*...*...............................................
..*...*..*..**...........*.....................................
.....*.**...*...........***....................................
....*.*.................*..*...................................
....*.*................*....*..................................
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.........*........**.*.....*...................................
....*...*****....**......**....................................
...*.*.......**..**.......**...................................
...*.......*.**................................................
....*........**................................................
.....*...****..................................................
..........***..................................................
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...........**..................................................
...........**..................................................
:cousins: (p3) This contains two copies of the {stillater} {rotor}.
.....*.**....
...***.*.*...
*.*......*...
**.**.**.*.**
...*.*....*.*
...*.*.***...
....**.*.....
:cover: The following {induction coil}. See {scrubber} for an example
of its use.
....*
..***
.*...
.*...
**...
:covered table: = {cap}
:cow: (c p8 fuse)
**.......**..**..**..**..**..**..**..**..**..**..**..**.....
**....*.***..**..**..**..**..**..**..**..**..**..**..**...**
....**.*.................................................*.*
....**...*************************************************..
....**.*..................................................*.
**....*.***..**..**..**..**..**..**..**..**..**..**..**..**.
**.......**..**..**..**..**..**..**..**..**..**..**..**.....
:CP pulsar: = {pulsar}
:crab: = {quarter}.
:crane: (c/4 diagonally, p4) The following {spaceship} found by Nicolay
Beluchenko in September 2005, a minor modification of a {tubeater}
found earlier by Hartmut Holzwart. The wing is of the same form as
in the {swan} and {Canada goose}.
.**.................
**..................
..*.................
....**...*..........
....**..*.*.........
.......**.*.........
.......**...........
.......**...........
.................**.
.........*....**.*..
.........***..**....
.........***..**....
..........**........
....................
............*.......
...........**.......
...........*........
............*.......
....................
.............**.....
..............*.**..
..................*.
...............**...
...............**...
.................*..
..................**
:cross: (p3) Found by Robert Wainwright in October 1989.
..****..
..*..*..
***..***
*......*
*......*
***..***
..*..*..
..****..
In February 1993, Hartmut Holzwart noticed that this is merely the
smallest of an infinite family of p3 oscillators. The next smallest
member is shown below.
..****.****..
..*..*.*..*..
***..***..***
*...........*
*...........*
***.......***
..*.......*..
***.......***
*...........*
*...........*
***..***..***
..*..*.*..*..
..****.****..
:crowd: (p3) Found by Dave Buckingham in January 1973.
...........*..
.........***..
.....**.*.....
.....*...*....
.......**.*...
...****...*...
*.*.....*.*.**
**.*.*.....*.*
...*...****...
...*.**.......
....*...*.....
.....*.**.....
..***.........
..*...........
:crown: The p12 part of the following p12 {oscillator}, where it is
{hassle}d by {caterer}, a {jam} and a {HW emulator}. This oscillator
was found by Noam Elkies in January 1995.
..........*...........
..........*......*....
...*....*...*...**....
...**....***..........
.........***..***..*.*
.*..***.........*.****
*.*.*...............**
*..*..................
.**........**.........
......**.*....*.**....
......*..........*....
.......**......**.....
....***..******..***..
....*..*........*..*..
.....**..........**...
:crucible: = {cauldron}
:crystal: A regular growth that is sometimes formed when a stream of
{glider}s, or other {spaceship}s, is fired into some junk.
The most common example is initiated by the following collision of
a glider with a {block}. With a glider stream of even {period} at
least 82, this gives a crystal which forms a pair {beehive}s for
every 11 gliders which hit it.
.*......
..*...**
***...**
:cuphook: (p3) Found by Rich Schroeppel, October 1970. This is one of
only three essentially different p3 {oscillator}s with only three
cells in the {rotor}. The others are {1-2-3} and {stillater}.
....**...
**.*.*...
**.*.....
...*.....
...*..*..
....**.*.
.......*.
.......**
The above is the original form, but it can be made more compact:
....**.
...*.*.
...*...
**.*...
**.*..*
...*.**
...*...
..**...
:curl: = {loop}
:dart: (c/3 orthogonally, p3) Found by David Bell, May 1992. A
25-glider recipe for the dart was found in December 2014 by Martin
Grant and Chris Cain, making it the first glider-constructible c/3
spaceship.
.......*.......
......*.*......
.....*...*.....
......***......
...............
....**...**....
..*...*.*...*..
.**...*.*...**.
*.....*.*.....*
.*.**.*.*.**.*.
:dead spark coil: (p1) Compare {spark coil}.
**...**
*.*.*.*
..*.*..
*.*.*.*
**...**
:de Bruijn diagram: = {de Bruijn graph}
:de Bruijn graph: As applied to Life, a de Bruijn graph is a graph
showing which pieces can be linked to which other pieces to form a
valid part of a Life pattern of a particular kind.
For example, if we are interested in {still life}s, then we could
consider 2x3 rectangular pieces and the de Bruijn graph would show
which pairs of these can be overlapped to form 3x3 squares in which
the centre cell remains unchanged in the next generation.
David Eppstein's search program {gfind} is based on de Bruijn
graphs.
:Deep Cell: A pattern by Jared James Prince, based on David Bell's
{unit Life cell}, in which each unit cell simulates two Life cells,
in such a way that a Life universe filled with Deep Cells simulates
two independent Life universes running in parallel.
In fact, a Life universe filled with Deep Cells can simulate
infinitely many Life universes, as follows. Let P_1, P_2, P_3, ...
be a sequence of Life patterns. Set the Deep Cells to run a
simulation of P_1 in parallel with a simulation of a universe filled
with Deep Cells, with these simulated Deep Cells running a simulation
of P_2 in parallel with another simulation of a universe filled with
Deep Cells, with these doubly simulated Deep Cells simulating P_3 in
parallel with yet another universe of Deep Cells, and so on.
Deep Cell is available from {http://psychoticdeath.com/life.htm}.
:Demonoid: The first self-constructing diagonal spaceship. A 0{hd}
Demonoid was completed by Chris Cain in December 2015, shortly after
a much larger 10{hd} version constructed the previous month in
collaboration with Dave Greene. The 0hd spaceship fits in a bounding
box about 55,000 cells square, and displaces itself by 65 cells
diagonally every 438,852 generations.
The first 0hd Demonoid was fired by a gun. As of this writing
(2017) this is the only case where a spaceship gun pattern was
completed before the first appearance of the actual spaceship.
:density: The density of a pattern is the limit of the proportion of
live cells in a (2n+1)x(2n+1) square centred on a particular cell as
n tends to infinity, when this limit exists. (Note that it does not
make any difference what cell is chosen as the centre cell. Also
note that if the pattern is finite then the density is zero.) There
are other definitions of density, but this one will do here.
In 1994 Noam Elkies proved that the maximum density of a stable
pattern is 1/2, which had been the conjectured value. See the paper
listed in the bibliography. Marcus Moore provided a simpler proof in
1995, and in fact proves that a {still life} with an m x n {bounding
box} has at most (mn+m+n)/2 cells.
But what is the maximum average density of an oscillating pattern?
The answer is conjectured to be 1/2 again, but this remains unproved.
The best upper bound so far obtained is 8/13 (Hartmut Holzwart,
September 1992).
The maximum possible density for a {phase} of an oscillating
pattern is also unknown. An example with a density of 3/4 is known
(see {agar}), but densities arbitrarily close to 1 may perhaps be
possible.
:dependent conduit: A {Herschel conduit} in which the input {Herschel}
interacts with catalysts in the first few ticks -- technically at
T=-3, before the Herschel is completely formed. Compare {independent
conduit}. The Herschel is prevented from emitting its {first natural
glider}, This is useful in cases where the previous conduit cannot
survive a first natural glider emitted from its output Herschel.
This term is somewhat confusing, since it is actually the previous
conduit that depends on the dependent conduit to suppress the
problematic glider. Dependent conduits such as the {F166} and
{Lx200} do not actually depend on anything. They can be freely
connected to any other conduits that fit, as long as the output
Herschel evolves from its standard great-grandparent. As of this
writing, the {Fx158} is the only known case where a conduit?output
Herschel has an alternate great-grandparent, which is incompatible
with dependent conduits' initial transparent block.
:destructor arm: A dedicated {construction arm} in the {Gemini}
spaceship, used only for removing previously active {circuit}ry once
it is no longer needed. More generally, any circuitry in a
self-constructing pattern dedicated exclusively to cleanup.
:D-heptomino: = {Herschel}
:diamond: = {tub}
:diamond ring: (p3) Found by Dave Buckingham in 1972.
......*......
.....*.*.....
....*.*.*....
....*...*....
..**..*..**..
.*....*....*.
*.*.**.**.*.*
.*....*....*.
..**..*..**..
....*...*....
....*.*.*....
.....*.*.....
......*......
:diehard: Any pattern that vanishes, but only after a long time. The
following example vanishes in 130 generations, which is probably the
limit for patterns of 7 or fewer cells. Note that there is no limit
for higher numbers of cells - e.g., for 8 cells we could have a
glider heading towards an arbitrarily distant blinker.
......*.
**......
.*...***
:dinner table: (p12) Found by Robert Wainwright in 1972.
.*...........
.***.......**
....*......*.
...**....*.*.
.........**..
.............
.....***.....
.....***.....
..**.........
.*.*....**...
.*......*....
**.......***.
...........*.
:dirty: Opposite of {clean}. A reaction which produces a large amount
of complicated junk which is difficult to control or use is said to
be dirty. Many basic {puffer engine}s are dirty and need to be
{tame}d by accompanying {spaceship}s in order to produce clean
output. Similarly, a dirty {conduit} is one that does not recover
perfectly after the passage of a {signal}; one or more extra {junk}
objects are left behind (or more rarely a {catalyst} is damaged) and
additional signals must be used to clean up the circuit before it can
be re-used.
:diuresis: (p90) Found by David Eppstein in October 1998. His original
stabilization used {pentadecathlon}s. The stabilization with
complicated {still life}s shown here (in two slightly different
forms) was found by Dean Hickerson the following day. The name is
due to Bill Gosper (see {kidney}).
.....**................**....
......*................*.....
......*.*............*.*.....
.......**............**......
.............................
....**..................**...
....*.*..........**....*.*...
.....*..........*.*.....*....
..*.............**.........*.
..******........*.....******.
.......*..............*......
....**..................**...
....*....................*...
.....*..................*....
..***..*..............*..***.
..*..***........*.....***...*
...*............**.......***.
....**..........*.*.....*....
......*..........**....*..**.
....**..................**.*.
.*..*....................*...
*.*.*..**............**..*...
.*..*.*.*............*.*.**..
....*.*................*..*..
.....**................**....
:dock: The following {induction coil}.
.****.
*....*
**..**
:domino: The 2-cell {polyomino}. A number of objects, such as the
{HWSS} and {pentadecathlon}, produce domino {spark}s.
:do-see-do: The following reaction, found by David Bell in 1996, in
which two {glider}s appear to circle around each other as they are
reflected 90 degrees by a {twin bees shuttle}. Four copies of the
reaction can be used to create a p92 glider loop which repeats the
do-see-do reaction forever.
.....................................................*.*
.....................................................**.
......................................................*.
........................................................
........................................................
........................................................
........................................................
........................................................
........................................................
........................................................
........................................................
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........................................................
........................................................
........................................................
................................................**......
................................................*.......
..............................................*.*.......
..............................................**........
..............................*.*.......................
..............................**........................
...............................*........................
........................................................
.......................***..............................
**........***........**.*.**............................
**........*...*.....*.....**............................
..........*....*.....**.*.**............................
...........*...*.......***..............................
........................................................
...........*...*........................................
..........*....*........................................
**........*...*............**...........................
**........***..............**...........................
:double-barrelled: Of a {gun}, emitting two streams of {spaceship}s (or
{rake}s). See {B-52 bomber} for an example.
:double block reaction: A certain reaction that can be used to
stabilize the {twin bees shuttle} (qv). This was discovered by David
Bell in October 1996.
The same reaction sometimes works in other situations, as shown in
the following diagram where a pair of blocks eats an {R-pentomino}
and a {LWSS}. (The LWSS version was known at least as early 1994,
when Paul Callahan saw it form spontaneously as a result of firing a
LWSS stream at some random junk.)
.****.....**....
*...*......**.**
....*......*..**
*..*............
................
.............**.
.............**.
:double caterer: (p3) Found by Dean Hickerson, October 1989. Compare
{caterer} and {triple caterer}.
.....**...*........
....*..*..***......
....**.*.....*.....
......*.****.*.....
..***.*.*...*.**...
.*..*..*...*..*.*..
*.*..*...*.**....*.
.*..........**.***.
..**.**.**...*.....
...*...*.....*.***.
...*...*......**..*
.................**
:double ewe: (p3) Found by Robert Wainwright before September 1971.
......**............
.......*............
......*.............
......**............
.........**.........
......***.*.........
*.**.*..............
**.*.*..............
.....*...*..........
....*...**....**....
....**....**...*....
..........*...*.....
..............*.*.**
..............*.**.*
.........*.***......
.........**.........
............**......
.............*......
............*.......
............**......
:double wing: = {moose antlers}. This term is no longer in use.
:dove: The following {induction coil}, found in 2015 to be a possible
active reaction for the input or output of a {converter}.
.**..
*..*.
.*..*
..***
:down boat with tail: = {cis-boat with tail}
:dragon: (c/6 orthogonally, p6) This {spaceship}, discovered by Paul
Tooke in April 2000, was the first known {c/6 spaceship}. With 102
cells, it was the smallest known orthogonal c/6 spaceship until
Hartmut Holzwart discovered {56P6H1V0} in April 2009.
.............*..**......*..***
.....*...****.******....*..***
.*****....*....*....***.......
*......**.*......**.***..*.***
.*****.***........****...*.***
.....*..*..............*......
........**..........**.**.....
........**..........**.**.....
.....*..*..............*......
.*****.***........****...*.***
*......**.*......**.***..*.***
.*****....*....*....***.......
.....*...****.******....*..***
.............*..**......*..***
:drain trap: = {paperclip}. This term is no longer in use.
:dried: = {freeze-dried}.
:drifter: A perturbation moving within a stable pattern. Dean
Hickerson has written a program to search for drifters, with the hope
of finding one which could be moved around a track. Because drifters
can be very small, they could be packed more tightly than
{Herschel}s, and so allow the creation of {oscillator}s of periods
not yet attained, and possibly prove that Life is {omniperiodic}.
Hickerson has found a number of components towards this end, but it
has proved difficult to change the direction of movement of a
drifter, and so far no complete track has been found. However,
Hickerson has had success using the same search program to find
{eater}s with novel properties, such as that used in {diuresis}.
:dual 1-2-3-4: = {Achim's p4}
:duoplet: A diagonal two-bit spark produced by many oscillators and
eater reactions. Among other uses, it can reflect gliders 90
degrees. The following pattern shows an {eater5} eating gliders and
producing duoplets which are then used to reflect a separate glider
stream.
..*....................
*.*....................
.**....................
.......................
.......................
.......*...............
.....*.*...............
......**...............
.....................*.
....................*..
....................***
.......................
.......................
................*......
...............*.......
...............***.....
.......................
....................**.
................*...**.
...............*.*.....
..............*.*......
..............*........
.............**........
:dying spark: See {spark}. A spark by definition dies out completely
after some number of ticks.
:early universe: Conway's somewhat confusing term for {sparse Life}.
:eater: Any {still life} that has the ability to interact with certain
patterns without suffering any permanent damage. (If it doesn't
suffer even temporary damage then it may be referred to as a {rock}.)
The {eater1} is a very common eater, and the term "eater" is often
used specifically for this object. Other eaters include {eater2},
{eater3}, {eater4} and even the humble {block}. (In fact the block
was the first known eater, being found capable of eating beehives
from a {queen bee}.) Another useful eater is shown below, feasting
on a glider.
...*.....
...*.*...
...**....
.........
.......**
...*...**
..*.*....
.*.*.....
.*.......
**.......
:eater1: (p1) Usually simply called an {eater}, and also called a
fishhook. Its ability to eat various objects was discovered by Bill
Gosper in 1971.
**..
*.*.
..*.
..**
:eater2: (p1) This {eater} was found by Dave Buckingham in the 1970s.
Mostly it works like the ordinary eater (see {eater1}) but with two
slight differences that make it useful despite its size: it takes
longer to recover from each bite, and it can eat objects appearing at
two different positions.
...*.**
.***.**
*......
.***.**
...*.*.
...*.*.
....*..
The first property means that, among other things, it can eat a
{glider} in a position that would destroy a fishhook. This novel
glider-eating action is occasionally of use in itself, and combined
with the symmetry means that an eater2 can eat gliders traveling
along four adjacent glider {lane}s, as shown below.
The following eater2 variant (Stephen Silver, May 1998) can be
useful for obtaining smaller {bounding box}es. A more compact
variant with the same purpose can be seen under {gliderless}.
.*.................
..*................
***................
...................
....*..............
.....*.............
...***.............
...................
.......*...........
........*..........
......***..........
...................
..........*........
...........*.....**
.........***......*
.............**.*..
.............**.**.
...................
.............**.**.
..............*.*..
..............*.*..
...............*...
:eater3: (p1) This large symmetric {eater}, found by Dave Buckingham,
has a very different eating action from the {eater1} and {eater2}.
The {loaf} can take bites out things, being flipped over in the
process. The rest of the object merely flips it back again.
.........**.
....**..*..*
.*..*....*.*
*.*.*.....*.
.*..*.**....
....*..*....
.....*....*.
......*****.
............
........*...
.......*.*..
........*...
:eater4: (p1) Another {eater} by Dave Buckingham, which he found in
1971, but did not recognize as an eater until 1975 or 1976. It can't
eat {glider}s, but it can be used for various other purposes. The
four NE-most centre cells regrow in a few generations after being
destroyed by taking a bite out of something.
...**.........
...*..........
**.*..........
*..**.........
.**....*......
...*****......
...*....**....
....**..*.....
......*.*.....
......*.*.*..*
.......**.****
.........*....
.........*.*..
..........**..
:eater5: (p1) A compound eater that can eat gliders coming from two
different directions. Also called the tub-with-tail eater (TWIT), it
is often placed along the edges of {glider lane}s to suppress
unwanted gliders in {conduit}s. Below is the standard form, a compact
form with a {long hook}, and an often-useful conjoined form found
with {Bellman}. The {sidesnagger} is a Spartan constellation that
has a similar glider-absorbing function, using a {loaf}. See also
{7x9 eater}.
.*.........*.........*...........
..*.........*.........*..........
***.......***.......***..........
.................................
......*.........*.........*......
.....*.........*.........*.......
.....***.......***.......***.....
.................................
..........**.....................
......*...**....*...**....*...**.
.....*.*.......*.*...*...*.*...*.
....*.*.......*.*...*....**...*..
....*.........*....*.........*...
...**........**.....***..*****.*.
......................*..*....*.*
...........................*..*.*
..........................**...*.
:eater/block frob: (p4) Found by Dave Buckingham in 1976 or earlier.
.**.......
..*.......
..*.*.....
...*.*....
.....**.**
........**
..**......
...*......
***.......
*.........
:eater-bound pond: = {biting off more than they can chew}
:eater-bound Z-hexomino: = {pentoad}
:eater eating eater: = {two eaters}
:eater plug: (p2) Found by Robert Wainwright, February 1973.
.......*
.....***
....*...
.....*..
..*..*..
.*.**...
.*......
**......
:eaters plus: = {French kiss}
:ecologist: (c/2 orthogonally, p20) This consists of the classic
{puffer train} with a {LWSS} added to suppress the debris. See also
{space rake}.
****.....**........
*...*...**.**......
*........****......
.*..*.....**.......
...................
.....*.........**..
...***........*****
..*...*.....*....**
..*....*****.....**
..**.*.****....**..
....*...**.***.....
.....*.*...........
...................
...................
****...............
*...*..............
*..................
.*..*..............
:edge-repair spaceship: A {spaceship} which has an edge that possesses
no {spark} and yet is able to {perturb} things because of its ability
to repair certain types of damage to itself. The most useful
examples are the following two small p3 {c/3 spaceship}s:
..................................*.....
........*.......................***.***.
.......****....................**......*
..*...*...**.**...........*...*..*...**.
.****.....*..**..........****...........
*...*.......*..*........*...*...........
.*.*..*..................*.*..*.........
.....*.......................*..........
These were found by David Bell in 1992, but the usefulness of the
edge-repair property wasn't recognised until July 1997. The
following diagram (showing an edge-repair spaceship deleting a
{Herschel}) demonstrates the self-repairing action.
................*.......
*..............****.....
*.*.......*...*...**.**.
***......****.....*..**.
..*.....*...*.......*..*
.........*.*..*.........
.............*..........
In October 2000, David Bell found that a {T-tetromino} component of a
{c/4 spaceship} can also be self-repairing. Stephen Silver noticed
that it could be used to delete beehives and, in November 2000, found
the smallest known c/4 spaceship with this edge-repair component - in
fact, two copies of the component:
.**..........................
*..*.........................
.**..........................
.............................
.......*.*...................
.......*.....................
.......*.*..*..*.............
..........*..................
...........*.**.*............
............***.*............
...........*....*..*.**......
........*...**...*.****......
........**..*..*.**....*....*
........*........**....*..***
.............**...**...*..**.
.**..........................
*..*.........................
.**..........................
:edge shooter: A {gun} which fires its gliders (or whatever) right at
the edge of the pattern, so that it can be used to fire them closely
parallel to others. This is useful for constructing complex guns.
Compare {glider pusher}, which can in fact be used for making edge
shooters.
The following diagram shows a p46 edge shooter found by Paul
Callahan in June 1994.
**............**..*....**..**.............
**............*.**......**.**.............
...............*......*.*.................
...............***....**..................
..........................................
...............***....**..................
...............*......*.*.................
**............*.**......**................
**............**..*....**.................
..........................................
..........................................
..........................................
..........................................
..........................................
..........................................
...............................***...***..
..............................*...*.*...*.
.............................*...**.**...*
.............................*.**.....**.*
...............................*.......*..
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...............................**.....**..
...............................**.....**..
:edge spark: A {spark} at the side of a {spaceship} that can be used to
{perturb} things as the spaceship passes by.
:edge sparker: A {spaceship} that produces one or more {edge spark}s.
:edgy: In {slow salvo} terminology, an edgy glider construction recipe
is one that places its final product at or very near the edge of its
{construction envelope}.
:egg: = {non-spark}. This term is no longer in use.
:E-heptomino: Name given by Conway to the following {heptomino}.
.***
**..
.**.
:elbow: This term may refer to a {signal elbow} or a {construction
elbow}. See also {elbow ladder}.
:elbow ladder: Scot Ellison's name for the type of pattern he created
in which one or more {glider}s shuttle back and forth (using the
{kickback reaction}) deleting the output gliders from a pair of
{slide gun}s.
:elbow operation: A recipe, usually a {glider salvo} traveling on one
or more {construction lane}s, that collides with an {elbow}
{constellation} and performs one of the standard transformations on
it -- {push}, {pull}, or {fire} for simple construction arms, along
with possible construct, duplicate-elbow, or delete-elbow ops for
more complicated systems. See {construction elbow}.
:electric fence: (p5) A stabilization of {ants}. Dean Hickerson,
February 1993.
..........*..................................................
.........*.*........................**.......................
..*....***.*.....*...................*...*..*......*.....**..
.*.*..*....**...*.*..................*.***..***...*.*....*...
.*.*..*.**.......*....................*...**...*.*..*......*.
**.**.*.*.*****.....*..................**...*..*.*.**.**..**.
.*.*..*...*..*..*.......**...**...**....**.**..*.*..*.*.*....
.*..**....**......***.**...**...**...***.....****.***.*...**.
..*..***..*..*.****...**...**...**...***.**..*....*.*....*..*
...**...*.*..*.....**...**...**...**......*............*...**
.....**.*.**.*.**..*......................*........**.*......
.....*.**.*..*.**....*.................**.*.*................
...........**.......**..................*..**................
......................................*.*....................
......................................**.....................
:elementary conduit: A {conduit} with no recognizable active signal
stage besides its input and output. Theoretically an elementary
conduit may become a composite conduit, if another conduit can be
found that shares the beginning or end of the conduit in question.
In practice this happens only rarely, because many of the most likely
branch points have already been identified: {glider}, standard *WSS
{spaceship}, {Herschel}, {B-heptomino}, {R-pentomino},
{pi-heptomino}, {queen bee shuttle}, {century} or {bookend}, {dove},
and {wing}.
:elevener: (p1)
**....
*.*...
..*...
..***.
.....*
....**
:Elkies' p5: (p5) Found by Noam Elkies in 1997.
.*.......
*..***...
..*......
...*.*..*
..**.****
....*....
....*.*..
.....**..
:emu: Dave Buckingham's term for a {Herschel loop} that does not emit
{glider}s (and so is "flightless"). All known Herschel loops of
periods 57, 58, 59 and 61 are emus. See also {Quetzal}.
:emulator: Any one of three p4 oscillators that produce {spark}s
similar to those produced by {LWSS}, {MWSS} and {HWSS}. See {LW
emulator}, {MW emulator} and {HW emulator}. Larger emulators are
also possible, but they require stabilizing objects to suppress their
{non-spark}s and so are of little use. The emulators were discovered
by Robert Wainwright in June 1980.
:engine: The active portion of an object (usually a {puffer} or {gun})
which is considered to actually produce its output, and which
generally permits no variation in how it works. The other parts of
the object are just there to support the engine. For examples, see
{puffer train}, {Schick engine}, {blinker puffer}, {frothing puffer}
and {line puffer}.
:en retard: (p3) Found by Dave Buckingham, August 1972.
.....*.....
....*.*....
**.*.*.*.**
.*.*...*.*.
*..*.*.*..*
.**.....**.
...**.**...
...*.*.*...
....*.*....
..*.*.*.*..
..**...**..
:Enterprise: (c/4 diagonally, p4) Found by Dean Hickerson, March 1993.
.......***...........
.....*.**............
....****.............
...**.....*..........
..***..*.*.*.........
.**...*.*..*.........
.*.*.*****...........
**.*.*...*...........
*........**..........
.**..*...*.*.........
....**..*.**......*..
...........**.....***
............*..***..*
............*..*..**.
.............*.**....
............**.......
............**.......
...........*.........
............*.*......
...........*..*......
.............*.......
:envelope: See {construction envelope}, {reaction envelope}.
:Eureka: (p30) A {pre-pulsar} {shuttle} found by Dave Buckingham in
August 1980. A variant is obtained by shifting the top half two
spaces to either side.
.*..............*.
*.*....*.......*.*
.*...**.**......*.
.......*..........
..................
..................
..................
.......*..........
.*...**.**......*.
*.*....*.......*.*
.*..............*.
:evolutionary factor: For an unstable pattern, the time to
stabilization divided by the initial {population}. For example, the
{R-pentomino} has an evolutionary factor of 220.6, while {bunnies}
has an evolutionary factor of 1925.777... The term is no longer in
use.
:exponential filter: A toolkit developed by Gabriel Nivasch in 2006,
enabling the construction of patterns with asymptotic population
growth matching O((log log ... log(t)) for any number of nested log
operations. See also {quadratic filter}, {recursive filter}.
:exposure: = {underpopulation}
:extensible: A pattern is said to be extensible if arbitrarily large
patterns of the same type can be made by repeating parts of the
original pattern in a regular way.
:extra extra long: = {long^4}
:extra long: = {long^3}
:extremely impressive: (p6) Found by Dave Buckingham, August 1976.
....**......
...*.***....
...*....*...
**.*...**...
**.*.....**.
....*****..*
..........**
......*.....
.....*.*....
......*.....
:F116: An {elementary conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Paul Callahan in February 1997. After 116
ticks, it produces a {Herschel} at (32, 1) relative to the input.
Its {recovery time} is 138 ticks; this can be reduced to 120 ticks by
adding extra mechanisms to suppress the internal glider. It is
{Spartan} only if the following conduit is a {dependent conduit}, so
that the {weld}ed {FNG} eater can be removed. A {ghost Herschel} in
the pattern below marks the output location:
........*..........................
........***........................
...........*.......................
..........**.......................
...................................
...................................
...................................
...................................
...................................
...................................
...................................
...................................
...................................
...................................
*..................................
*.*.............................*..
***.............................*..
..*.............................***
..................................*
...................................
...................................
...................................
...................................
.........................**........
...................**.....*........
...................*.*.***.........
............**.......*.*...........
............**.......**............
:F117: A {composite conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Dave Buckingham in July 1996. It is made up
of two {elementary conduit}s, HFx58B + {BFx59H}. After 117 ticks, it
produces a {Herschel} at (40, -6) relative to the input. Its
{recovery time} is 63 ticks. It can be made {Spartan} by replacing
the {snake} with an {eater1} in one of two orientations. A {ghost
Herschel} in the pattern below marks the output location:
......................**.....................
.......................*.....................
..........*...........*......................
..........***.........**.....................
.............*...............................
**..........**...............................
.*...........................................
.*.*.........................................
..**.........................................
.........................**...............*..
.........................**...............*..
..........................................***
............................................*
.............................................
.............................................
..*..........................................
..*.*........................................
..***........................................
....*...........**...........................
................*............................
.................***.........................
...................*.........................
:F166: An {elementary conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Paul Callahan in May 1997. The F166 and
{Lx200} conduits are the two original {dependent conduit}s (several
more have since been discovered). After 166 ticks, it produces a
{Herschel} at (49, 3) relative to the input. Its {recovery time} is
116 ticks. A {ghost Herschel} in the pattern below marks the output
location:
.................................**.....................
..................................*.....................
.................................*......................
.................................**.....................
........................................................
........................................................
.**.....................................................
***.**..................................................
.**.***.**..............................................
***.**..**..........................**...............*..
**..................................**...............*..
.....................................................***
.......................................................*
........................................................
........................................................
........................................................
......**................................................
.....*.*......................................**........
.....*.........................................*........
....**.........................**...........***.........
...............................**...........*...........
........................................................
........................................................
.................**.....................................
..................*.....................................
...............***......................................
...............*........................................
...........................**...........................
...........................*............................
............................***.........................
..............................*.........................
The F166 can be made {Spartan} by replacing the {snake} with an
{eater1} in one of two orientations. The input shown here is a
{Herschel great-grandparent}, since the input reaction is catalysed
by the {transparent} block before the Herschel's standard form can
appear.
:F171: An {elementary conduit}, the seventeenth {Herschel conduit},
discovered by Brice Due in August 2006 in a search using only
{eater}s as {catalyst}s. This was the first new Herschel conduit
discovery since 1998. After 171 ticks, it produces a {Herschel} at
(29, -17) relative to the input. Its {recovery time} is 227 ticks,
slower than many of the original sixteen conduits because of the
delayed destruction of a temporary blinker, though it is clearly
{Spartan}. A {ghost Herschel} in the pattern below marks the output
location:
..........*......................
..........***....................
.............*...................
............**...................
.....*...........................
.....***.........................
........*........................
.......**........................
.................................
..............................*..
....**........................*..
.....*........................***
.....*.*........................*
......**.........................
.................................
.................................
*................................
***..............................
...*.............................
..**.............................
.................................
.................................
.................................
.................................
.................................
.................................
.*...............................
.*.*.............................
.***.............................
...*.............................
.................................
..........**.....................
...........*.....................
........***......................
........*........................
:factory: Another word for {gun}, but not used in the case of glider
guns. The term is also used for a pattern that repeatedly
manufactures objects other than {spaceship}s or {rake}s. In this
case the new objects do not move out of the way, and therefore must
be used up in some way before the next one is made. The following
shows an example of a p144 gun which consists of a p144 block factory
whose output is converted into gliders by a p72 oscillator. (This gun
is David Bell's improvement of the one Bill Gosper found in July
1994. The p72 oscillator is by Robert Wainwright, 1990, and the
block factory is {Achim's p144} minus one of its stabilizing blocks.)
.......................**........................**
.......................**........................**
.........................................**........
........................................*..*.......
.........................................**........
...................................................
....................................***............
....................................*.*............
.........**.........................***............
.........**.........................**.............
........*..*.......................***.............
........*..*.**....................*.*.............
........*....**....................***.............
..........**.**....................................
...............................**..................
.....................**.......*..*.................
.....................**........**..................
.................................................**
.................................................**
...................................................
....**..................*..........................
**....****..........**..**.***.....................
**..**.***..........**....****.....................
....*...................**.........................
:familiar fours: Common patterns of four identical objects. The five
commonest are {traffic light} (4 blinkers), {honey farm} (4
beehives), {blockade} (4 blocks), {fleet} (4 ships, although really 2
ship-ties) and {bakery} (4 loaves, although really 2 bi-loaves).
:fanout: A mechanism that emits two or more objects of some type for
each one that it receives. Typically the objects are {glider}s or
{Herschel}s; {glider duplicator}s are a special case.
:Fast Forward Force Field: The following reaction found by Dieter
Leithner in May 1994. In the absence of the incoming LWSS the
gliders would simply annihilate one another, but as shown they allow
the LWSS to advance 11 spaces in the course of the next 6
generations. A neat illusion. See also {star gate}. (Leithner
named the Fast Forward Force Field in honour of his favourite science
fiction writer, the physicist Robert L. Forward.)
.......*......*..
........*......**
..**..***.....**.
**.**............
****.........*...
.**.........**...
............*.*..
:father: = {parent}
:fd: Abbreviation for {full diagonal}s.
:featherweight spaceship: = {glider}
:fencepost: Any pattern that stabilizes one end of a {wick}.
:Fermat prime calculator: A pattern constructed by Jason Summers in
January 2000 that exhibits {infinite growth} if and only if there are
no Fermat primes greater than 65537. The question of whether or not
it really does exhibit infinite growth is therefore equivalent to a
well-known and long-standing unsolved mathematical problem. It will,
however, still be growing at generation 10^2585827975. The pattern is
based on Dean Hickerson's {primer} and {caber tosser} patterns and a
p8 {beehive} {puffer} by Hartmut Holzwart.
:F-heptomino: Name given by Conway to the following {heptomino}.
**..
.*..
.*..
.***
:figure-8: (p8) Found by Simon Norton in 1970.
***...
***...
***...
...***
...***
...***
:filter: Any {oscillator} used to delete some but not all of the
{spaceship}s in a stream. An example is the {blocker}, which can be
positioned so as to delete every other {glider} in a stream of period
8n+4, and can also do the same for {LWSS} streams. Other examples
are the {MW emulator} and {T-nosed p4} (either of which can be used
to delete every other LWSS in a stream of period 4n+2), the
{fountain} (which does the same for {MWSS} streams) and a number of
others, such as the p6 {pipsquirter}, the {pentadecathlon} and the
p72 oscillator shown under {factory}. Another example, a p4
oscillator deleting every other HWSS in a stream of period 4n+2, is
shown below. (The p4 oscillator here was found, with a slightly
larger {stator}, by Dean Hickerson in November 1994.)
..........****............
....**...******...........
****.**..****.**..........
******.......**...........
.****.....................
..........................
................**........
..............*....*......
..........................
.............*.*..*.*.....
...........****.**.****...
........*.*....*..*....*.*
........**.**.*....*.**.**
...........*.*......*.*...
........**.*.*......*.*.**
........**.*..........*.**
...........*.*.****.*.*...
...........*.*......*.*...
..........**.*.****.*.**..
..........*..***..***..*..
............*..****..*....
...........**.*....*.**...
...........*..*....*..*...
............*..*..*..*....
.............**....**.....
:finger: A protruding cell in an {oscillator} or {dying spark}, with
the ability to modify a nearby active reaction. Like a {thumb}, a
finger cell appears at the edge of a reaction envelope and is the
only live cell in its row or column. The finger spark remains alive
for two ticks before dying, whereas a thumb cell dies after one tick.
:fire: an encoded signal used in combination with {push} and {pull}
{elbow operation}s in a simple {construction arm}. When a FIRE
signal is sent, the construction-arm elbow produces an output glider,
usually at 90 degrees from the construction arm. This terminology is
generally used when there is only a single recipe for such a glider
output, or only one recipe for each glider color (e.g., FIRE WHITE,
FIRE BLACK).
:fireship: (c/10 orthogonally, p10) A variant of the {copperhead} with
a trailing component that emits several large {spark}s, discovered by
Simon Ekstrom on 20 March 2016. The interaction between the
copperhead and the additional component is minimal enough that the
extension technically fits the definition of a {tagalong}. However,
the extension slightly modifies two of the {phase}s of the spaceship,
starting two ticks after the phase shown below, so it's also valid to
classify the fireship as a distinct spaceship.
....**....
...****...
..........
..******..
...****...
..........
..**..**..
**.*..*.**
...*..*...
..........
..........
....**....
....**....
..........
.*.*..*.*.
*..*..*..*
*........*
*........*
**......**
..******..
:fire-spitting: (p3) Found by Nicolay Beluchenko, September 2003.
...*......
.***......
*.........
.*.***....
.*.....*..
..*..*....
..*.*..*.*
........**
:first natural glider: The glider produced at T=21 during the evolution
of a {Herschel}. This is the most common signal output from a
{Herschel conduit}.
:fish: A generic term for {LWSS}, {MWSS} and {HWSS}, or, more
generally, for any {spaceship}.
:fishhook: = {eater1}
:fleet: (p1) A common formation of two {ship-tie}s.
....**....
....*.*...
.....**...
.......**.
**.....*.*
*.*.....**
.**.......
...**.....
...*.*....
....**....
:flip-flop: Any p2 {oscillator}. However, the term is also used in two
more specific (and non-equivalent) senses: (a) any p2 oscillator
whose two {phase}s are mirror images of one another, and (b) any p2
oscillator in which all {rotor} cells die from {underpopulation}. In
the latter sense it contrasts with {on-off}. The term has also been
used even more specifically for the 12-cell flip-flop shown under
{phoenix}.
:flip-flops: Another name for the flip-flop shown under {phoenix}.
:flipper: Any {oscillator} or {spaceship} that forms its mirror image
halfway through its period.
:flotilla: A {spaceship} composed of a number of smaller interacting
spaceships. Often one or more of these is not a true spaceship and
could not survive without the support of the others. The following
example shows an {OWSS} escorted by two {HWSS}.
....****.......
...******......
..**.****......
...**..........
...............
...........**..
.*............*
*..............
*.............*
**************.
...............
...............
....****.......
...******......
..**.****......
...**..........
:fly: A certain c/3 {tagalong} found by David Bell, April 1992. Shown
here attached to the back of a small spaceship (also by Bell).
..*...............................
.*.*..............................
.*.*......................*.*...*.
.*.......................**.*.*..*
...........***........*.........*.
**.........**..*.**...*..****.....
.*.*.........****..*.*..**....**..
.**........*..*...***.....***.....
..*.......*....*..**..**..*..*....
...*..*...*....*..***.*.*....**...
.......*.**....*..****.....*......
....**...**....*..****.....*......
....*.*...*....*..***.*.*....**...
...**.....*....*..**..**..*..*....
....*.*....*..*...***.....***.....
.....*.......****..*.*..**....**..
...........**..*.**...*..****.....
...........***........*.........*.
.........................**.*.*..*
..........................*.*...*.
:flying machine: = {Schick engine}
:FNG: = {first natural glider}.
:fore and back: (p2) Compare {snake pit}. Found by Achim Flammenkamp,
July 1994.
**.**..
**.*.*.
......*
***.***
*......
.*.*.**
..**.**
:forward glider: A {glider} which moves at least partly in the same
direction as the {puffer}(s) or {spaceship}(s) under consideration.
:fountain: (p4) Found by Dean Hickerson in November 1994, and named by
Bill Gosper. See also {filter} and {superfountain}.
.........*.........
...................
...**.*.....*.**...
...*.....*.....*...
....**.**.**.**....
...................
......**...**......
**...............**
*..*...*.*.*...*..*
.***.*********.***.
....*....*....*....
...**.........**...
...*...........*...
.....*.......*.....
....**.......**....
:fourteener: (p1)
....**.
**..*.*
*.....*
.*****.
...*...
:fox: (p2) This is the smallest asymmetric p2 oscillator. Found by
Dave Buckingham, July 1977.
....*..
....*..
..*..*.
**.....
....*.*
..*.*.*
......*
:freeze-dried: A term used for a {glider-constructible} {seed} that can
activated in some way to produce a complex object. For example, a
"freeze-dried salvo" is a constellaton of constructible objects
which, when {trigger}ed by a single glider, produces a unidirectional
glider {salvo}, and nothing else. Freeze-dried salvos can be useful
in {slow salvo} constructions, especially when an active circuit has
to destroy or reconstruct itself in a limited amount of time.
Gradual modification by a {construction arm} may be too slow, or the
circuit doing the construction may itself be the object that must be
modified.
The concept may be applied to other types of objects. For example,
one possible way to build a gun for a {waterbear} would be to program
a construction arm to build a freeze-dried waterbear seed, and then
trigger it when the construction is complete.
:French kiss: (p3) Found by Robert Wainwright, July 1971.
*.........
***.......
...*......
..*..**...
..*....*..
...**..*..
......*...
.......***
.........*
For many years this was one of the best-known small oscillators with
no known {glider synthesis}. In October 2013 Martin Grant completed
a 23-glider construction.
:frog II: (p3) Found by Dave Buckingham, October 1972.
..**...**..
..*.*.*.*..
....*.*....
...*.*.*...
...**.**...
.**.....**.
*..*.*.*..*
.*.*...*.*.
**.*...*.**
....***....
...........
...*.**....
...**.*....
:frothing puffer: A frothing puffer (or a frothing spaceship) is a
{puffer} (or {spaceship}) whose back end appears to be unstable and
breaking apart, but which nonetheless survives. The exhaust festers
and clings to the back of the puffer/spaceship before breaking off.
The first known frothing puffers were c/2, and most were found by
slightly modifying the back ends of p2 spaceships. A number of these
have periods which are not a multiple of 4 (as with some {line
puffer}s). Paul Tooke has also found c/3 frothing puffers.
The following p78 c/2 frothing puffer was found by Paul Tooke in
April 2001.
.......*.................*.......
......***...............***......
.....**....***.....***....**.....
...**.*..***..*...*..***..*.**...
....*.*..*.*...*.*...*.*..*.*....
.**.*.*.*.*....*.*....*.*.*.*.**.
.**...*.*....*.....*....*.*...**.
.***.*...*....*.*.*....*...*.***.
**.........**.*.*.*.**.........**
............*.......*............
.........**.*.......*.**.........
..........*...........*..........
.......**.*...........*.**.......
.......**...............**.......
.......*.*.*.***.***.*.*.*.......
......**...*...*.*...*...**......
......*..*...*.*.*.*...*..*......
.........**....*.*....**.........
.....**....*...*.*...*....**.....
.........*.**.*...*.**.*.........
..........*.*.*.*.*.*.*..........
............*..*.*..*............
...........*.*.....*.*...........
:frothing spaceship: See {frothing puffer}.
:frozen: = {freeze-dried}.
:full diagonal: Diagonal distance measurement, abbreviated "fd", often
appropriate when a {construction arm} {elbow} or similar
diagonally-adjustable mechanism is present.
:fumarole: (p5) Found by Dean Hickerson in September 1989. In terms of
its 7x8 bounding box this is the smallest p5 oscillator.
...**...
.*....*.
.*....*.
.*....*.
..*..*..
*.*..*.*
**....**
:fuse: A {wick} burning at one end. For examples, see {baker}, {beacon
maker}, {blinker ship}, {boat maker}, {cow}, {harvester}, {lightspeed
wire}, {pi ship}, {reverse fuse}, {superstring} and {washerwoman}.
Useful fuses are usually {clean}, but see also {reburnable fuse}.
:Fx119: An {elementary conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Dave Buckingham in September 1996. After
119 ticks, it produces an inverted {Herschel} at (20, 14) relative to
the input. Its recovery time is 231 ticks; this can be reduced
somewhat by suppressing the output Herschel's glider, or by adding
extra {catalyst}s to make the reaction settle more quickly. A {ghost
Herschel} in the pattern below marks the output location:
*......................
*.*....................
***....................
..*....................
.......................
.......................
.......................
.......................
.......................
.......................
.......................
.......................
.......................
.......................
.......................
.........**...........*
....**...**.........***
....**..............*..
....................*..
.......................
...**..................
....*....**............
.***.....**............
.*.....................
:Fx119 inserter: A {Herschel-to-glider} {converter} and {edge shooter}
based on an {Fx119} Herschel conduit:
.........*....................
.........*.*..................
.........***..................
...........*..................
..............................
..............................
..............................
..............................
..**......**..................
...*.......*..................
***.....***...................
*.......*.....................
..............................
..............................
..............................
..................**..........
.............**...**..........
.............**...............
..............................
..............................
............**............**..
.............*....**......*...
..........***.....**.......***
..........*..................*
:Fx153: A {composite conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Paul Callahan in February 1997. It is made
up of two {elementary conduit}s, HF94B + {BFx59H}. After 153 ticks,
it produces an inverted {Herschel} at (48, -4) relative to the input.
Its {recovery time} is 69 ticks. It can be made {Spartan} by
replacing the {snake} with an {eater1} in one of two orientations. A
{ghost Herschel} in the pattern below marks the output location:
.........................**..........................
**........................*..........................
.*.............**......***...........................
.*.*...........**......*.............................
..**.................................................
.....................................................
.....................................................
.....................................................
....................................................*
..................................................***
.................................**...............*..
..*..............................**...............*..
..*.*................................................
..***................................................
....*................................................
.....................................................
.....................................................
..............................**.....................
..............................*......................
...........**...**.............*.....................
............*...*.............**.....................
.........***.....***.................................
.........*.........*.................................
:Fx158: An {elementary conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Dave Buckingham in July 1996. After 158
ticks, it produces an inverted {Herschel} at (27, -5) relative to the
input. Its {recovery time} is 176 ticks. It is the only known small
conduit that does not produce its output Herschel via the usual
{Herschel great-grandparent}, so it cannot be followed by a
{dependent conduit}. A {ghost Herschel} in the pattern below marks
the output location:
.........*....**..............
........*.*..*.*.......**.....
.......*..****.........*......
.......*.*....*......*.*......
.....***.**..**......**.......
....*.........................
.*..****.**...................
.***...*.**...................
....*.........................
...**.........................
..............................
..............................
..............................
..............................
..............................
..............................
.............................*
...........................***
...........................*..
...........................*..
*.............................
*.*...........................
***...........................
..*...........................
..............................
...............**.............
.........**....*.*............
..........*......*............
.......***.......**...........
.......*......................
:Fx176: A {composite conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Paul Callahan in October 1997. It is made
up of three {elementary conduit}s, HF95P + PF35W + WFx46H. After 176
ticks, it produces an inverted {Herschel} at (45, 0) relative to the
input. Its {recovery time} is 92 ticks. A {ghost Herschel} in the
pattern below marks the output location:
..............................**..................
..............................**..................
..................................................
.................**...............................
..................*...............................
..................*.*.............................
...................**.............................
..................................................
..................................................
..............**..................................
......*.......**..................................
......***.........................................
.........*........................................
........**........................................
..................................................
**................................................
.*................................................
.*.*.....................................**.......
..**......................................*.......
..........................................*.*.....
...........................................*.*....
............................................*...**
................................................**
..................................................
..................................................
..*...............................................
..*.*...............................**...........*
..***...............................**.........***
....*..........................................*..
...............................................*..
..............**........**........................
..............**..**.....*........................
..................*.*.***.........................
....................*.*...........................
....................**....**......................
.........................*.*....**................
.........................*......**................
........................**........................
:Fx77: An {elementary conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Dave Buckingham in August 1996. After 77
ticks, it produces an inverted {Herschel} at (25, -8) relative to the
input. Its {recovery time} is 61 ticks; this can be reduced slightly
by suppressing the output Herschel's glider, as in the {L112} case.
A {pipsquirter} can replace the blinker-suppressing eater to produce
an extra glider output. It is one of the simplest known {Spartan}
conduits, and one of the few {elementary conduit}s in the original
set of sixteen.
In January 2016, Tanner Jacobi discovered a {Spartan} method of
extracting an extra glider output (top variant below). A {ghost
Herschel} marks the output location for each variant.
.*............................
.***..........................
....*.........................
...**...........**...........*
................**.........***
...........................*..
...........................*..
..............................
..............................
..............................
..*...........................
..*.*.........................
..***.........................
....*.........................
..............................
..............................
..............................
..............................
..............................
............**......**........
...........*..*.....**........
...........*..*...............
............**................
..............................
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..............................
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..............................
*.............................
***...........................
...*..........................
..**...........**...........*.
...............**.........***.
..........................*...
..........................*...
..............................
..............................
..............................
.*............................
.*.*..........................
.***..........................
...*..........................
..............................
..............................
..............................
..............................
..............................
................**............
................*.*...........
..................*...........
..................**..........
:Gabriel's p138: (p138) The following {oscillator} found by Gabriel
Nivasch in October 2002.
.......***.....
......*..*.....
.......*...*...
..*.....***....
...*.....*.....
**.**..........
*..*.........*.
*.*.........*.*
.*.........*..*
..........**.**
.....*.....*...
....***.....*..
...*...*.......
.....*..*......
.....***.......
:galaxy: = {Kok's galaxy}
:Game of Life: = {Life}
:Game of Life News: A blog reporting on new Life discoveries, started
by Heinrich Koenig in December 2004, currently found at
{http://pentadecathlon.com/lifenews/}.
:Garden of Eden: A configuration of ON and OFF cells that can only
occur in generation 0. (This term was first used in connection with
cellular automata by John W. Tukey, many years before Life.) It was
known from the start that there are Gardens of Eden in Life, because
of a theorem by Edward Moore that guarantees their existence in a
wide class of cellular automata. Explicit examples have since been
constructed, the first by Roger Banks, et al. at MIT in 1971. This
example was 9 x 33. In 1974 J. Hardouin-Duparc et al. at the
University of Bordeaux 1 produced a 6 x 122 example. The following
shows a 12 x 12 example found by Nicolay Beluchenko in February 2006,
based on a 13 x 12 one found by Achim Flammenkamp in June 2004.
..*.***.....
**.*.*****.*
*.*.**.*.*..
.****.*.***.
*.*.**.***.*
.***.**.*.*.
..*...***..*
.*.**.*.*.*.
***.****.*.*
**.****...*.
.*.*.**..*..
.**.*..**.*.
Below is a 10x10 Garden of Eden found by Marijn Heule, Christiaan
Hartman, Kees Kwekkeboom, and Alain Noels in 2013 using SAT-solver
techniques. An exhaustive search of 90-degree rotationally symmetric
10x10 patterns was possible because the symmetry reduces the number
of unknown cells by a factor of four.
.*.***.*..
..*.*.*..*
*.***..**.
.*.*****.*
*..*..****
****..*..*
*.*****.*.
.**..***.*
*..*.*.*..
..*.***.*.
Steven Eker has since found several asymmetrical Gardens of Eden
that are slightly smaller than this in terms of bounding box area.
:Gemini: ((5120,1024)c/33699586 obliquely, p33699586) The first
{self-constructing} spaceship, and also the first {oblique}
spaceship. It was made public by Andrew Wade on 18 May 2010. It was
the thirteenth explicitly constructed spaceship velocity in Life, and
made possible an infinite family of related velocities. The Gemini
spaceship derives its name from the Latin "gemini", meaning twins,
describing its two identical halves, each of which contains three
Chapman-Greene {construction arm}s. A tape of gliders continually
relays between the two halves, instructing each to delete its parent
and construct a daughter configuration.
:Gemini puffer: See {Pianola breeder}.
:Geminoid: A type of self-constructing circuitry that borrows key ideas
from Andrew Wade's {Gemini} spaceship, but with several
simplifications. The main feature common to the Gemini spaceship is
the construction recipe encoding method. Information is stored
directly, and much more efficiently, in the timings of moving
gliders, rather than in a static tape with 1s and 0s encoded by the
presence of small stationary objects.
Unlike the original Gemini, Geminoids have {ambidextrous}
construction arms, initially using glider pairs on two lanes
separated by 9{hd}, 10hd, or 0hd. The design was the basis for Dave
Greene's {linear propagator} and the {Demonoid}s. A more recent
development is a Geminoid toolkit using a {single-channel}
construction arm, which allows for the possibility of multiple elbows
with no loss of efficiency, or the construction of temporary lossless
elbows. Compare {slow elbow}.
Other new developments that could be considered part of the
extended "Geminoid" toolkit include {freeze-dried} construction
salvos and seeds, used when objects must be built within a short time
window, and self-destruct circuits, which are used as an alternative
to a {destructor arm} to clean up temporary objects in a similarly
short window.
:generation: The fundamental unit of time. The starting pattern is
generation 0.
:germ: (p3) Found by Dave Buckingham, September 1972.
....**....
.....*....
...*......
..*.****..
..*....*..
.**.*.....
..*.*.****
*.*.*....*
**...***..
.......**.
:gfind: A program by David Eppstein which uses {de Bruijn graph}s to
search for new {spaceship}s. It was with gfind that Eppstein found
the {weekender}, and Paul Tooke later used it to find the {dragon}.
It is available at {http://www.ics.uci.edu/~eppstein/ca/gfind.c} (C
source code only).
Compare {lifesrc}.
:ghost Herschel: A dying {spark} made by removing one cell from the
{Herschel} heptomino. This particular spark has the advantage that,
when placed in a conduit to mark the location of an input or output
Herschel, it disappears cleanly without damaging adjacent catalysts,
even in {dependent conduit}s with a block only two cells away.
*..
*..
***
..*
:GIG: A glider injection gate. This is a device for injecting a
{glider} into a glider stream. The injected glider is synthesized
from one or more incoming {spaceship}s assisted by the presence of
the GIG. (This contrasts with some other glider injection reactions
which do not require a GIG.) Gliders already in the glider stream
pass through the GIG without interfering with it. A GIG usually
consists of a small number of oscillators.
Glider injection gates are useful for building glider {gun}s with
{pseudo}-periods that are of the form nd, where n is a positive
integer, and d is a proper divisor of some convenient base gun period
(such as 30 or 46), with d > 13.
:glasses: (p2) Compare {scrubber} and {spark coil}.
....*........*....
..***........***..
.*..............*.
.*..***....***..*.
**.*...*..*...*.**
...*...****...*...
...*...*..*...*...
....***....***....
..................
....**.*..*.**....
....*.**..**.*....
:glider: (c/4 diagonally, p4) The smallest, most common and first
discovered {spaceship}. This was found by Richard Guy in 1970 while
Conway's group was attempting to track the evolution of the
{R-pentomino}. The name is due in part to the fact that it is {glide
symmetric}. (It is often stated that Conway discovered the glider,
but he himself has said it was Guy. See also the cryptic reference
("some guy") in {Winning Ways}.)
***
*..
.*. The term "glider" is also occasionally (mis)used to mean
"spaceship".
:glider-block cycle: An infinite {oscillator} based on the following
reaction (a variant of the {rephaser}). The oscillator consists of
copies of this reaction displaced 2n spaces from one another (for
some n>6) with blocks added between the copies in order to cause the
reaction to occur again halfway through the period. The period of
the resulting infinite oscillator is 8n-20. (Alternatively, in a
cylindrical universe of width 2n the oscillator just consists of two
gliders and two blocks.)
...**...
...**...
........
........
..*..*..
*.*..*.*
.**..**.
:glider constructible: See {glider synthesis}.
:glider construction: = {glider synthesis}.
:glider duplicator: Any reaction in which one input {glider} is
converted into two output gliders. This can be done either by
{oscillator}s or by {spaceship}s. The most useful glider duplicators
are those with low {period}s.
The following period 30 glider duplicator demonstrates a simple
glider duplicating mechanism found by Dieter Leithner. The input
glider stream comes in from the upper left, and the output glider
streams leave at the upper and lower right. One of the output glider
streams is inverted, so an {inline inverter} is required to complete
the duplicator.
..........*.*.......................
...........**.......................
...........*........................
....................................
....................................
....................................
........................**....*.....
..................*.....**....**....
...................**........*.*....
..................**................
....................................
....................................
....................................
....................................
......................**............
.......................**...........
............*.........*.............
............*.*.....................
.............*.*.........**.........
**...........*..*.......***.........
**...........*.*.....*.**...........
............*.*......*..*...........
............*........*.**...........
........................***.....**..
.........................**.....*.*.
..................................*.
..................................**
Spaceship {convoy}s which can duplicate gliders are very useful
since they (along with {glider turner}s) provide a means to clean up
many dirty puffers by duplicating and turning output gliders so as to
impact into the exhaust to clean it up.
Glider duplicators (and turners) are known for backward gliders
using p2 c/2 spaceships, and for forward gliders using p3 c/3
spaceships. These are the most general duplicators for these speeds.
:glider gun: A {gun} which fires {glider}s.
:glider injection gate: = {GIG}
:glider lane: See {lane}.
:gliderless: A {gun} is said to be gliderless if it does not use
{glider}s. The purist definition would insist that a glider does not
appear anywhere, even incidentally. For a long time the only known
way to construct {LWSS}, {MWSS} and {HWSS} guns involved gliders, and
it was not until April 1996 that Dieter Leithner constructed the
first gliderless gun (a p46 LWSS gun).
The following diagram shows the p44 MWSS gun that Dieter Leithner
discovered (in a somewhat larger form) in April 1997. This is the
smallest known gliderless gun, and also the smallest known MWSS gun.
It is based on an important p44 oscillator discovered by Dave
Buckingham in early 1992, shown here in an improved form found in
January 2005 by Jason Summers using a new p4 {sparker} by Nicolay
Beluchenko. Note that a glider shape appears in this gun for three
consecutive generations, but always as part of a larger {cluster}, so
even a purist would regard this gun as gliderless.
.......*..........................................
..**...*.*....*...................................
..*..**..*.*.**.*..***..**........................
....**.......**.*.*.**..**........................
...***.......*.......***.........*................
.......................*.......***................
.......................*......*........***........
..............................**.......*..*.......
.........**..............*.............*..........
.........**.............*..............*...*......
.........................**............*..........
........................*.*.............*.*.......
..................................................
.......................*.*.....***................
........................*.....*..*..............**
**............***.......*......**...........**.*.*
**...........*...*..........................**.*..
.............**.**..............................*.
.................................**.........**.**.
..............................**.............*.*..
.............................................*.*..
..............................................*...
.............**.**.............*.*................
**...........*...*.............**.................
**............***.................................
...........................**.....................
...........................*.*....................
.............................*....................
.............................**...................
..................................................
.........**.......................................
.........**.......................................
..................................................
.......................*..........................
.......................*..........................
...***.......*.......***..........................
....**.......**.*.*.**..**........................
..*..**..*.*.**.*..***..**........................
..**...*.*....*...................................
.......*..........................................
:glider pair: Two gliders traveling in the same direction on fixed
lanes, with a specific spacetime offset. In a {transceiver} the
preferred term is {tandem glider}. For several years, glider pairs
were the standard building blocks in {Geminoid} {construction arm}s,
until the discovery of {single-channel} construction toolkits.
:glider pusher: An arrangement of a {queen bee shuttle} and a
{pentadecathlon} that can push the path of a passing glider out by
one half-diagonal space. This was found by Dieter Leithner in
December 1993 and is shown below. It is useful for constructing
complex {gun}s where it may be necessary to produce a number of
gliders travelling on close parallel paths. See also {edge shooter}.
.........**..............
.........**..............
.........................
..........*..............
.........*.*.............
.........*.*.............
..........*..............
.........................
.........................
.......**.*.**...........
.......*.....*...........
........*...*............
.*.......***.............
..*......................
***......................
.........................
.........................
.................*....*..
...............**.****.**
.................*....*..
:glider recipe: = {glider synthesis}.
:glider reflector: See {reflector}.
:gliders by the dozen: (stabilizes at time 184) In early references
this is usually shown in a larger form whose generation 1 is
generation 8 of the form shown here.
**..*
*...*
*..**
:glider synthesis: Construction of an object by means of {glider}
collisions. It is generally assumed that the gliders should be
arranged so that they could come from infinity - that is, gliders
should not have had to pass through one another to achieve the
initial arrangement.
Glider syntheses for all {still life}s and known {oscillator}s with
at most 14 cells were found by Dave Buckingham.
Perhaps the most interesting glider syntheses are those of
{spaceship}s, because these can be used to create corresponding
{gun}s and {rake}s. Many of the c/2 spaceships that are based on
{standard spaceship}s have been synthesized, mostly by Mark Niemiec.
In June 1998 Stephen Silver found syntheses for some of the
{Cordership}s (although it was not until July 1999 that Jason Summers
used this to build a Cordership gun). In May 2000, Noam Elkies
suggested that a 2c/5 spaceship found by Tim Coe in May 1996 might be
a candidate for glider synthesis. Initial attempts to construct a
synthesis for this spaceship got fairly close, but it was only in
March 2003 that Summers and Elkies managed to find a way to perform
the crucial last step. Summers then used the new synthesis to build
a c/2 forward rake for the 2c/5 spaceship; this was the first example
in Life of a rake which fires spaceships that travel in the same
direction as the rake but more slowly.
A 3-glider synthesis of a {pentadecathlon} is shown in the diagram
below. This was found in April 1997 by Heinrich Koenig and came as a
surprise, as it was widely assumed that anything using just three
gliders would already be known.
......*...
......*.*.
......**..
..........
***.......
..*.......
.*.....**.
........**
.......*..
:glider train: A certain p64 c/2 orthogonal {puffer} that produces two
rows of {block}s and two backward {glider} waves. Ten of these were
used to make the first {breeder}.
..............................*............
...............................*...........
.........................*.....*...........
....*.....................******.....******
.....*..............................*.....*
*....*....................................*
.*****..............................*....*.
......................................**...
...........................................
.....................................*.....
....................................*......
...................................**...**.
...................................*.*...**
....................................*...**.
........................................*..
...........................................
........................................*..
....................................*...**.
...................................*.*...**
...................................**...**.
....................................*......
.....................................*.....
...........................................
......................................**...
.*****..............................*....*.
*....*....................................*
.....*..............................*.....*
....*.....................******.....******
.........................*.....*...........
...............................*...........
..............................*............
:glider turner: An reaction in which a {glider} is turned by an
{oscillator} or a {spaceship}. In the former case, the glider turner
is usually called a {reflector}.
Glider turners are easily built using {standard spaceship}s. The
following diagram shows a convoy which turns a {forward glider} 90
degrees, with the new glider also moving forwards.
.........**.........
........**.****.....
.*.......******.....
*.........****......
***.................
....................
....................
....................
....................
...*................
.*...*..............
*...................
*....*..............
*****...............
....................
....................
.............******.
.............*.....*
.............*......
..............*....*
................**..
Small rearrangements of the back two spaceships can alternatively
send the output glider into any of the other three directions.
See also {glider duplicator} and {reflector}.
:glide symmetric: Undergoing simultaneous reflection and translation. A
glide symmetric {spaceship} is sometimes called a {flipper}.
:Gn: An abbreviation specific to {converter}s that produce multiple
{glider}s. A "G" followed by any integer value means that the
converter produces a {tandem glider} -- two parallel glider outputs
with lanes separated by the specified number of {half diagonal}s.
:gnome: = {fox}
:GoE: = {Garden of Eden}
:GoL: = {Game of Life}
:Golly: A cross-platform open source Life program by Andrew Trevorrow
and Tomas Rokicki. Unlike most Life programs it includes the ability
to run patterns using the {hashlife} algorithm. It is available from
{http://golly.sourceforge.net}.
:Gosper glider gun: The first known {gun}, and indeed the first known
finite pattern with unbounded growth, found by Bill Gosper in
November 1970. This period 30 gun remains the smallest known gun in
terms of its bounding box, though some variants of the p120 {Simkin
glider gun} have a lower population. Gosper has since found other
guns, see {new gun} and the p144 gun shown under {factory}.
........................*...........
......................*.*...........
............**......**............**
...........*...*....**............**
**........*.....*...**..............
**........*...*.**....*.*...........
..........*.....*.......*...........
...........*...*....................
............**......................
:Gotts dots: A 41-cell 187x39 {superlinear growth} pattern found by
Bill Gosper in March 2006, who named it in honour of Nick Gotts,
discoverer of many other low-population superlinear patterns, such as
{Jaws}, {mosquito}s, {teeth}, {catacryst} and {metacatacryst}.
Collisions within the pattern cause it to sprout its Nth {switch
engine} at generation T = ~224n-6. The population of the pattern at
time t is asymptotically proportional to t times log(t), so the
growth rate is O(t ln(t)), faster than {linear growth} but slower
than {quadratic growth}.
:gourmet: (p32) Found by Dave Buckingham in March 1978. Compare with
{pi portraitor} and {popover}.
..........**........
..........*.........
....**.**.*....**...
..*..*.*.*.....*....
..**....*........*..
................**..
....................
................**..
*.........***..*.*..
***.......*.*...*...
...*......*.*....***
..*.*..............*
..**................
....................
..**................
..*........*....**..
....*.....*.*.*..*..
...**....*.**.**....
.........*..........
........**..........
:gp: {glider pair}
:grammar: A set of rules for connecting components together to make an
object such as a {spaceship}, {oscillator} or {still life}.
:grandfather: = {grandparent}
:grandparent: A pattern is said to be a grandparent of the pattern it
gives rise to after two generations. See also {parent}.
:Gray counter: (p4) Found in 1971. If you look at this in the right
way you will see that it cycles through the Gray codes from 0 to 3.
Compare with {R2D2}.
......*......
.....*.*.....
....*.*.*....
.*..*...*..*.
*.*.*...*.*.*
.*..*...*..*.
....*.*.*....
.....*.*.....
......*......
:gray ship: = {grey ship}
:great on-off: (p2)
..**....
.*..*...
.*.*....
**.*..*.
....**.*
.......*
....***.
....*...
:grey counter: = {Gray counter} (This form is erroneous, as Gray is
surname, not a colour.)
:grey ship: A {spaceship} that contains a region with an average
density of 1/2, and which is {extensible} in such a way that the
region of average density 1/2 can be made larger than any given
square region.
See also {with-the-grain grey ship}, {against-the-grain grey ship}
and {hybrid grey ship}.
:grin: The following common {parent} of the {block}. This name relates
to the infamous {Cheshire cat}. See also {pre-block}.
*..*
.**.
:grow-by-one object: A pattern whose population increases by one cell
every generation. The smallest known grow-by-one object is the
following 44-cell pattern (David Bell's one-cell improvement of a
pattern found by Nicolay Beluchenko, September 2005).
........**.......
.......**........
.........*.......
...........**....
..........*......
.................
.........*..**...
.**.....**....*..
**.....*.....*...
..*....*.*...**..
....*..*....**.*.
....**.......**..
........*....*.**
.......*.*..*.**.
........*........
:growing/shrinking line ship: A {line ship} in which the line
repeatedly grows and shrinks, resulting in a high-period {spaceship}.
:growing spaceship: An object that moves like a {spaceship}, except
that its front part moves faster than its back part and a {wick}
extends between the two. Put another way, a growing spaceship is a
{puffer} whose output is burning {clean}ly at a slower rate than the
puffer is producing it. Examples include {blinker ship}s and {pi
ship}s.
:gull: = {elevener}
:gun: Any stationary pattern that emits {spaceship}s (or {rake}s)
forever. For examples see {double-barrelled}, {edge shooter},
{factory}, {gliderless}, {Gosper glider gun}, {Simkin glider gun},
{new gun} and {true}.
:gunstar: Any of a series of glider {gun}s of period 144+72n (for all
non-negative integers n) constructed by Dave Buckingham in 1990 based
on his {transparent block reaction} and Robert Wainwright's p72
oscillator (shown under {factory}).
:half-baked knightship: ((6,3)c/2621440, p2621440) An
adjustable-period, fixed-direction {macro-spaceship} based on the
{half-bakery reaction}. This was the first spaceship based on this
reaction, constructed in December 2014 by Adam Goucher. It moves 6
cells horizontally and 3 cells vertically every 2621440+8N ticks,
depending on the relative spacing of the two halves. It is one of
the slowest known {knightship}s, and the first one that was not a
{Geminoid}. Chris Cain optimized the design a few days later to
create the {Parallel HBK}.
The spaceship produces gliders from near-diagonal lines of
half-bakeries, which collide with each other at 180 degrees. These
collisions produce {monochromatic salvo}s that gradually build and
trigger {seed}s, which in turn eventually construct small
synchronized salvos of gliders. These re-activate the lines of
half-bakeries, thus closing the cycle and moving the entire spaceship
obliquely by (6,3).
:half bakery: = {bi-loaf}.
:half-bakery reaction: the key reaction used in the {half-baked
knightship} and {Parallel HBK}, where a half-bakery is moved by (6,3)
when a glider collides with it, and the glider continues on a new
lane. Ivan Fomichev noticed in May 2014 that pairs of these
reactions at the correct relative spacing can create 90-degree output
gliders:
.............................*.
............................*..
............................***
...............................
...............................
...............................
...............................
...............................
...............................
...............................
....................**.........
...................*..*........
...................*.*.........
.................**.*..........
........*.......*..*...........
......**........*.*............
.......**........*.............
...............................
....**.........................
...*..*........................
...*.*.........................
.**.*..........................
*..*...........................
*.*............................
.*.............................
:half diagonal: A natural measurement of distance between parallel
glider lanes, or between {elbow} locations in a {universal}
{construction arm} {elbow operation} library. If two gliders are in
the same phase and exactly lined up vertically or horizontally, N
cells away from each other, then the two glider {lane}s are
considered to be N half diagonals (hd) apart. Gliders that are an
integer number of {full diagonal}s apart must be the same colour,
whereas integer {half diagonal}s allow for both glider colours. See
{colour of a glider}, {linear propagator}.
:half fleet: = {ship-tie}
:Halfmax: A pattern that acts as a spacefiller in half of the Life
plane, found by Jason Summers in May 2005. It expands in three
directions at c/2, producing a triangular region that grows to fill
half the plane.
:hammer: To hammer a {LWSS}, {MWSS} or {HWSS} is to smash things into
the rear end of it in order to transform it into a different type of
{spaceship}. A hammer is the object used to do the hammering. In the
following example by Dieter Leithner a LWSS is hammered by two more
LWSS to make it into a MWSS.
*..*................
....*...**..........
*...*..***.....****.
.****..**.*....*...*
........***....*....
.........*......*..*
:hammerhead: A certain front end for {c/2 spaceship}s. The central
part of the hammerhead pattern is supported between two {MWSS}. The
picture below shows a small example of a {spaceship} with a
hammerhead front end (the front 9 columns).
................*..
.**...........*...*
**.***.......*.....
.*****.......*....*
..*****.....*.****.
......***.*.**.....
......***....*.....
......***.***......
..........**.......
..........**.......
......***.***......
......***....*.....
......***.*.**.....
..*****.....*.****.
.*****.......*....*
**.***.......*.....
.**...........*...*
................*..
:hand: Any object used as a {slow salvo} {target} by a {construction
arm}.
:handshake: An old MIT name for {lumps of muck}, from the following
form (2 generations on from the {stairstep hexomino}):
..**.
.*.**
**.*.
.**..
:harbor: (p5) Found by Dave Buckingham in September 1978. The name is
by Dean Hickerson.
.....**...**.....
.....*.*.*.*.....
......*...*......
.................
.....**...**.....
**..*.*...*.*..**
*.*.**.....**.*.*
.*.............*.
.................
.*.............*.
*.*.**.....**.*.*
**..*.*...*.*..**
.....**...**.....
.................
......*...*......
.....*.*.*.*.....
.....**...**.....
:harvester: (c p4 fuse) Found by David Poyner, this was the first
published example of a {fuse}. The name refers to the fact the it
produces debris in the form of {block}s which contain the same number
of cells as the fuse has burnt up.
................**
...............*.*
..............*...
.............*....
............*.....
...........*......
..........*.......
.........*........
........*.........
.......*..........
......*...........
.....*............
*****.............
****..............
*.**..............
:hashlife: A Life algorithm by Bill Gosper that is designed to take
advantage of the considerable amount of repetitive behaviour in many
large patterns of interest. It provides a means of evolving
repetitive patterns millions (or even billions or trillions) of
generations further than normal Life algorithms can manage in a
reasonable amount of time.
The hashlife algorithm is described by Gosper in his paper listed
in the bibliography at the end of this lexicon. Roughly speaking,
the idea is to store subpatterns in a hash table so that the results
of their evolution do not need to be recomputed if they arise again
at some other place or time in the evolution of the full pattern.
This does, however, mean that complex patterns can require
substantial amounts of memory.
Tomas Rokicki and Andrew Trevorrow implemented Hashlife into
{Golly} in 2005.
:hassle: See {hassler}.
:hassler: An {oscillator} that works by hassling (repeatedly moving or
changing) some object. For some examples, see {Jolson}, {baker's
dozen}, {toad-flipper}, {toad-sucker} and {traffic circle}.
:hat: (p1) Found in 1971. See also {twinhat} and {sesquihat}.
..*..
.*.*.
.*.*.
**.**
:HBK: {half-baked knightship}
:hd: Abbreviation for {half diagonal}. This metric is used primarily
for relative measurements of glider lanes, often in relation to
{self-constructing} circuitry; compare {Gn}.
:heat: For an {oscillator} or {spaceship}, the average number of cells
which change state in each generation. For example, the heat of a
{glider} is 4, because 2 cells are born and 2 die every generation.
For a period n oscillator with an r-cell {rotor} the heat is at
least 2r/n and no more than r(1-(n mod 2)/n). For n=2 and n=3 these
bounds are equal.
:heavyweight emulator: = {HW emulator}
:heavyweight spaceship: = {HWSS}
:heavyweight volcano: = {HW volcano}
:hebdarole: (p7) Found by Noam Elkies, November 1997. Compare
{fumarole}. The smaller version shown below was found soon after by
Alan Hensel using a component found by Dave Buckingham in June 1977.
The top tens rows can be stabilized by their mirror image (giving an
{inductor}) and this was the original form found by Elkies.
...........**...........
....**...*....*...**....
.*..*..*.*....*.*..*..*.
*.*.*.**.*....*.**.*.*.*
.*..*..*.*.**.*.*..*..*.
....**....*..*....**....
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.......*..*..*..*.......
......*.**....**.*......
.......*........*.......
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...**..............**...
...*..****....****..*...
....*.*.*.*..*.*.*.*....
...**.*...****...*.**...
.......**......**.......
.........**..**.........
.........*..*.*.........
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:hectic: (p30) Found by Robert Wainwright in September 1984.
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:Heisenburp device: A pattern which can detect the passage of a
{glider} without affecting the glider's path or timing. The first
such device was constructed by David Bell in December 1992. The term
is due to Bill Gosper.
The following is an example of the kind of reaction used at the
heart of a Heisenburp device. The glider at bottom right alters the
reaction of the other two gliders without itself being affected in
any way.
*.....*....
.**...*.*..
**....**...
...........
...........
...........
.........**
........*.*
..........*
:helix: A convoy of {standard spaceship}s used in a {Caterpillar} to
move some piece of debris at the speed of the Caterpillar. The
following diagram illustrates the idea. The leading edge of this
example helix, represented by the glider at the upper right in the
pattern below, moves at a speed of 65c/213, or slightly faster than
c/4.
...............................*.............
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.........***....*.**...*..*....***..***......
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Adjustable-speed helices can produce a very wide range of spaceship
speeds; see {Caterloopillar}.
:heptaplet: Any 7-cell {polyplet}.
:heptapole: (p2) The {barberpole} of length 7.
**........
*.*.......
..........
..*.*.....
..........
....*.*...
..........
......*.*.
.........*
........**
:heptomino: Any 7-cell {polyomino}. There are 108 such objects. Those
with names in common use are the {B-heptomino}, the {Herschel} and
the {pi-heptomino}.
:Herschel: (stabilizes at time 128) The following pattern which occurs
at generation 20 of the {B-heptomino}.
*..
***
*.*
..*
The name is commonly ascribed to the Herschel heptomino's
similarity to a planetary symbol. William Herschel discovered Uranus
in 1781. However, in point of fact a Herschel bears no particular
resemblance to either of the symbols used for Uranus, but does
closely resemble the symbol for Saturn. So the appropriate name might
actually be "Huygens" -- but "Herschel" is now universally used by
tradition.
Herschels are one of the most versatile types of {signal} in stable
circuitry. {R-pentomino}es and {B-heptomino}es naturally evolve into
Herschels, and {converter}s have also been found that change
{pi-heptomino}es and several other signal types into Herschels, and
vice versa. See {elementary conduit}.
:Herschel climber: Any {reburnable fuse} reaction involving
{Herschel}s. May refer specifically to the {(23,5)c/79 Herschel
climber} used in the {waterbear}, or one of several similar reactions
with various velocities. See also {Herschel-pair climber}.
:Herschel conduit: A {conduit} that moves a {Herschel} from one place
to another. See also {Herschel loop}.
Well over a hundred simple stable Herschel conduits are currently
known. As of August 2017 the number is approximately 130, depending
on the precise definition of "simple" -- e.g., fitting inside a
100x100 bounding box, and producing output in no more than 300
{tick}s. In general a Herschel conduit can be called "simple" if its
active reaction does not return to a Herschel stage except at its
output. Compare {elementary conduit}, {composite conduit}.
The original {universal} set consisted of sixteen stable Herschel
conduits, discovered between 1995 and 1998 by Dave Buckingham (DJB)
and Paul Callahan (PBC). These are shown in the following table. In
this table, the number in "name/steps" is the number of {tick}s
needed to produce an output Herschel from the input Herschel. "m"
tells how the Herschel is moved (R = turned right, L = turned left, B
= turned back, F = unturned, f = flipped), and "dx" and "dy" give the
displacement of the centre cell of the Herschel (assumed to start in
the orientation shown above).
-----------------------------------------
name/steps m dx dy discovery
-----------------------------------------
{R64} R -11 9 DJB, Sep 1995
{Fx77} Ff -25 -8 DJB, Aug 1996
{L112} L -12 -33 DJB, Jul 1996
{F116} F -32 1 PBC, Feb 1997
{F117} F -40 -6 DJB, Jul 1996
{Bx125} Bf 9 -17 PBC, Nov 1998
{Fx119} Ff -20 14 DJB, Sep 1996
{Fx153} Ff -48 -4 PBC, Feb 1997
{L156} L -17 -41 DJB, Aug 1996
{Fx158} Ff -27 -5 DJB, Jul 1996
{F166} F -49 3 PBC, May 1997
{Fx176} Ff -45 0 PBC, Oct 1997
{R190} R -24 16 DJB, Jul 1996
{Lx200} Lf -17 -40 PBC, Jun 1997
{Rx202} Rf -7 32 DJB, May 1997
{Bx222} Bf 6 -16 PBC, Oct 1998
-----------------------------------------
See also {Herschel transceiver}.
:Herschel descendant: A common active pattern occurring at generation
22 of a {Herschel}'s evolution:
**..
*.**
...*
.*.*
.**.
There are other evolutionary paths leading to the same pattern,
including the modification of a {B-heptomino} implied by generation
21 of a Herschel.
:Herschel great-grandparent: A specific three-{tick} predecessor of a
{Herschel}, commonly seen in {Herschel conduit} collections that
contain {dependent conduit}s. In some situations -- e.g., when the
collection contains conduits intended to be evolved individually --
it is helpful to display the input reaction in this form instead of
the standard Herschel form.
.**....
***.**.
.**.***
***.**.
**.....
Dependent conduit inputs are catalysed by a {transparent} block
before the Herschel's standard form can appear, and before the
Herschel's {first natural glider} is produced. This means that these
conduits will fail if an actual Herschel is placed in the "correct"
input location for a dependent conduit. Refer to {F166} or {Lx200}
to see the correct relative placement of the standard transparent
block catalyst.
Almost all known Herschel conduits produce a Herschel
great-grandparent near the end of their evolutionary sequence. In
the original {universal} set of Herschel conduits, {Fx158} is the
only exception.
:Herschel loop: A cyclic {Herschel track}. Although no loop of length
less than 256 generations has been constructed it is possible to make
{oscillator}s of smaller periods by putting more than one Herschel in
the track. In this way oscillators, and in most cases {gun}s, of all
periods from 54 onwards can now be constructed (although the p55 case
is a bit strange, shooting itself with gliders in order to stabilize
itself). See also {emu} and {omniperiodic}.
:Herschel-pair climber: Any {reburnable fuse} reaction involving pairs
of {Herschel}s. May refer specifically to the {31c/240 Herschel-pair
climber} used in the {Centipede}, or one of several similar reactions
with various velocities. See also {Herschel climber}.
:Herschel receiver: Any {circuit} that converts a {tandem glider} into
a Herschel signal. The following diagram shows a pattern found by
Paul Callahan in 1996, as part of the first stable glider
{reflector}. Used as a receiver, it converts two parallel input
gliders (with path separations of 2, 5, or 6) to an {R-pentomino},
which is then converted to a Herschel by one of two known mechanisms
(the first of which was found by Dave Buckingham way back in 1972,
and the second by Stephen Silver in October 1997). The version using
Buckingham's R-to-Herschel converter is shown below.
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:Herschel-to-glider: The largest category of {elementary conduit}.
Gliders are very common and self-supporting, so it's much easier to
find these than any other type of output {signal}. A large
collection of these H-to-G {converter}s has been compiled, with many
different output {lane}s and timings. These can be used to
synchronize multiple signals to produce {gun} patterns or complex
logic circuitry. See {NW31T120} for an example.
:Herschel track: A {track} for {Herschel}s. See also {B track}.
:Herschel transceiver: An adjustable {Herschel conduit} made up of a
{Herschel transmitter} and a {Herschel receiver}. The intermediate
stage consists of a {tandem glider} -- two {glider}s on parallel
{lane}s -- so that the transmitter and receiver can be separated by
any required distance. The conduit may be {stable}, or may contain
low-period {oscillator}s.
:Herschel transmitter: Any {Herschel}-to-two-{glider} {converter} that
produces a {tandem glider} that can be used as input to a {Herschel
receiver}. If the gliders are far enough apart, and if one of the
gliders is used only for cleanup, then the transmitter is
{ambidextrous}: with a small modification to the receiver, a
suitably oriented mirror image of the receiver will also work.
The following diagram shows a {stable} Herschel transmitter found
by Paul Callahan in May 1997:
......**...........
.....*.*...........
...***.............
..*...*......*.....
..**.**......***...
.............*.*...
...............*...
...................
...................
**.*...............
*.**...............
...................
...................
...................
...............**..
...............*...
................***
..................*
Examples of small reversible p6 and p7 transmitters are also known,
and more recently several alternate {Herschel transceiver}s have been
found with different lane spacing, e.g., 0, 2, 4, 6, and 13.
:Hertz oscillator: (p8) Compare {negentropy}, and also {cauldron}.
Found by Conway's group in 1970.
...**.*....
...*.**....
...........
....***....
...*.*.*.**
...*...*.**
**.*...*...
**.*...*...
....***....
...........
....**.*...
....*.**...
:hexadecimal: = {beehive and dock}
:hexaplet: Any 6-cell {polyplet}.
:hexapole: (p2) The {barberpole} of length 6.
**.......
*.*......
.........
..*.*....
.........
....*.*..
.........
......*.*
.......**
:hexomino: Any 6-cell {polyomino}. There are 35 such objects. For some
examples see {century}, {stairstep hexomino}, {table}, {toad} and
{Z-hexomino}.
:H-heptomino: Name given by Conway to the following {heptomino}. After
one generation this is the same as the {I-heptomino}.
**..
.*..
.***
..*.
:high-bandwidth telegraph: (p960, p30 circuitry) A variant of the
{telegraph} constructed by Louis-Francois Handfield in February 2017,
using periodic components to achieve a transmission rate of one bit
per 192 ticks. The same ten signals are sent as in the original
telegraph and the {p1 telegraph}, but information is encoded more
efficiently in the timing of those signals. Specifically, the new
transmitter sends five bits every 960 ticks by adjusting the relative
timings inside each of the five mirror-image paired subunits of the
composite signal in the beehive-chain {lightspeed wire} {fuse}.
:highway robber: any mechanism that can retrieve a signal from a
spaceship {lane} while allowing spaceships on nearby lanes to pass by
unaffected. In practice the spaceship is generally a glider. The
signal is removed from the lane, an output signal is generated
elsewhere, and the highway robber returns to its original state. A
competent highway robber does not affect gliders even on the lane
adjacent to the affected glider stream, except during its recovery
period.
A perfect highway robber doesn't affect later gliders even in the
lane to which it is attached, even during its recovery period. Below
is a near-perfect highway robber "bait" that requires three
synchronized signals to rebuild (the {Herschel}, {B-heptomino}, and
{glider}.) The glider at the top right passes by unharmed, but
another glider following on the same {lane} 200 ticks later will be
cleanly reflected to a new path -- and another glider following that
one will also pass by unharmed. The only imperfection is a few ticks
at the very end of the reconstruction, as the beehive is being
rebuilt::
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:hive: = {beehive}
:hivenudger: (c/2 orthogonally, p4) A {spaceship} found by Hartmut
Holzwart in July 1992. (The name is due to Bill Gosper.) It
consists of a {pre-beehive} escorted by four {LWSS}. In fact any
LWSS can be replaced by a {MWSS} or a {HWSS}, so that there are 45
different single-hive hivenudgers.
****.....*..*
*...*...*....
*.......*...*
.*..*...****.
.............
.....**......
.....**......
.....**......
.............
.*..*...****.
*.......*...*
*...*...*....
****.....*..*
Wider versions can be made by stabilizing the front of the extended
"pre-beehive", as in the {line puffer} shown below.
.........*.*..................
........*..*..................
.......**.....................
......*...*...................
.....***.*....................
..**..........................
.*...*****.......****.....*..*
*...*............*...*...*....
*.....**.........*.......*...*
***...****........*..*...****.
.*.......*....................
.**...................**......
.*.*..................**......
.**..**.*........*.*..**......
..*.***.*...*.****.*..**......
.........**.*.**..*...**...***
....******.**...****..**...***
.....*....***......*..**...***
......**.....**..**...**......
.......*..*.....****..**......
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..................*..*...****.
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:honeycomb: (p1)
..**..
.*..*.
*.**.*
.*..*.
..**..
:honey farm: (p1) A common formation of four beehives.
......*......
.....*.*.....
.....*.*.....
......*......
.............
.**.......**.
*..*.....*..*
.**.......**.
.............
......*......
.....*.*.....
.....*.*.....
......*......
:hook: Another term for a {bookend}. It is also used for other
hook-shaped things, such as occur in the {eater1} and the {hook with
tail}, for example.
:hook with tail: (p1) For a long time this was the smallest {still
life} without a well-established name. It is now a vital component
of the smallest known {HWSS} {gun}, where it acts as a {rock}.
*.*..
**.*.
...*.
...**
:houndstooth agar: The p2 {agar} that results from tiling the plane
with the following pattern.
.***
.*..
..*.
***.
:house: The following {induction coil}. It is generation 3 of the
{pi-heptomino}. See {spark coil} and {dead spark coil}.
.***.
*...*
**.**
:H-to-G: A {Herschel-to-glider} {converter}.
:H-to-MWSS: A {Spartan} {converter} found by Tanner Jacobi in October
2015, which convertes an input {Herschel} to a middleweight
spaceship. The key discovery was a very small but slightly {dirty}
H-to-MWSS conduit, where a Herschel is catalyzed to produce an {MWSS}
but also leaves behind a beehive. Prefixing two {R64} conduits to
this produces a {composite} converter that successfully deletes the
beehive in advance, using the input Herschel's {first natural
glider}.
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There are many other ways to remove the beehive using a spare glider
or additional conduits, but they are generally less compact than
this.
:hustler: (p3) Found by Robert Wainwright, June 1971.
.....**....
.....**....
...........
...****....
*.*....*...
**.*...*...
...*...*.**
...*....*.*
....****...
...........
....**.....
....**.....
:hustler II: (p4)
....*...........
....***.........
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*.**.*.**..*....
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.....*....*.....
....*.....*.*.**
....*..**.*.**.*
.....**..*......
........*.......
.........***....
...........*....
:HW emulator: (p4) Found by Robert Wainwright in June 1980. See also
{emulator}.
.......**.......
..**.*....*.**..
..*..........*..
...**......**...
***..******..***
*..*........*..*
.**..........**.
:HWSS: (c/2 orthogonally, p4) A heavyweight spaceship, the fourth most
common {spaceship}. Found by Conway in 1970 by modifying a {LWSS}.
See also {MWSS}.
...**..
.*....*
*......
*.....*
******.
:HWSS emulator: = {HW emulator}
:HW volcano: (p5) A p5 {domino} {sparker}, found by Dean Hickerson in
February 1995.
.........*..........................
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.....*....**.*......................
.....*.**...**......**..............
....**.*.**.........*.*.............
.........*.*****......*..*.**.......
..*.**.**.*.....*....**.*.**.*......
.....**.....****........*....*......
*...*.*..*...*.*....**.*.****.**....
*...*.*..**.*.**.**....*.*....*.*...
.....**...***.**.*.***.*..***...*...
..*.**.**.**.............*.*..*.*.**
...........*......*.*.*.*..**.*.*.*.
....**.*.*.**......**.*.*.*...*.*.*.
.....*.**.*..*.......*.**..****.**..
.....*....*.*........*...**.........
....**....**........**...*..*.......
...........................**.......
At least four progressively smaller forms of this sparker have been
found, including a 25-cell-wide version found by David Eppstein in
2003, and a vertically narrower 28-cell-wide version by Karel Suhajda
in 2004. Scot Ellison's 17-cell-wide version is shown in the
{zweiback} entry.
:hybrid grey ship: A {grey ship} containing more than one type of
region of density 1/2, usually a combination of a {with-the-grain
grey ship} and an {against-the-grain grey ship}.
:I-heptomino: Name given by Conway to the following {heptomino}. After
one generation this is the same as the {H-heptomino}.
**..
.*..
.**.
..**
:IMG: = {intermitting glider gun}
:Immigration: A form of {colourised Life} in which there are two types
of ON cell, a newly-born cell taking the type of the majority of its
three {parent cells} and surviving cells remaining of the same type
as in the previous generation.
:independent conduit: A {Herschel conduit} in which the input Herschel
produces its {first natural glider}. Compare {dependent conduit}.
:induction coil: Any object used to stabilize an edge (or edges)
without touching. The tubs used in the {Gray counter} are examples,
as are the blocks and snakes used in the {Hertz oscillator} and the
heptomino at the bottom of the {mathematician}.
:inductor: Any {oscillator} with a row of dead cells down the middle
and whose two halves are mirror images of one another, both halves
being required for the oscillator to work. The classic examples are
the {pulsar} and the {tumbler}. If still lifes are considered as p1
oscillators then there are numerous simple examples such as {table on
table}, {dead spark coil} and {cis-mirrored R-bee}. Some spaceships,
such as the {brain}, the {snail} and the {spider} use the same
principle.
:infinite glider hotel: A pattern by David Bell, named after Hilbert's
"infinite hotel" scenario in which a hotel with an infinite number of
rooms has room for more guests even if it is already full, simply by
shuffling the old guests around.
In this pattern, two pairs of {Cordership}s moving at c/12 are
pulling apart such that there is an ever-lengthening {glider} track
between them. Every 128 generations another glider is injected into
the glider track, joining the gliders already circulating there. The
number of gliders in the track therefore increases without limit.
The tricky part of this construction is that even though all the
previously injected gliders are repeatedly flying through the
injection point, that point is guaranteed to be empty when it is time
for the next glider to be injected.
:infinite growth: Growth of a finite pattern such that the {population}
tends to infinity, or at least is unbounded. Sometimes the term is
used for growth of something other than population (for example,
length), but here we will only consider infinite population growth.
The first known pattern with infinite growth in this sense was the
{Gosper glider gun}.
An interesting question is: What is the minimum population of a
pattern that exhibits infinite growth? In 1971 Charles Corderman
found that a {switch engine} could be stabilized by a {pre-block} in
a number of different ways, giving 11-cell patterns with infinite
growth. This record stood for more than quarter of a century until
Paul Callahan found, in November 1997, two 10-cell patterns with
infinite growth. The following month he found the one shown below,
which is much neater, being a single {cluster}. This produces a
stabilized switch engine of the block-laying type.
......*.
....*.**
....*.*.
....*...
..*.....
*.*.....
Nick Gotts and Paul Callahan have also shown that there is no
infinite growth pattern with fewer than 10 cells, so that the
question has now been answered.
Also of interest is the following pattern (again found by
Callahan), which is the only 5x5 pattern with infinite growth. This
too emits a block-laying switch engine.
***.*
*....
...**
.**.*
*.*.*
Following a conjecture of Nick Gotts, Stephen Silver produced, in
May 1998, a pattern of width 1 which exhibits infinite growth. This
pattern was very large (12470x1 in the first version, reduced to
5447x1 the following day). In October 1998 Paul Callahan did an
exhaustive search, finding the smallest example, the 39x1 pattern
shown below. This produces two block-laying switch engines,
stability being achieved at generation 1483.
********.*****...***......*******.*****
Although the simplest infinite growth patterns grow at a rate that
is (asymptotically) linear, many other types of growth rate are
possible, {quadratic growth} (see also {breeder}) being the fastest.
Dean Hickerson has found many patterns with unusual growth rates,
such as {sawtooth}s and a {caber tosser}. Another pattern with
superlinear but non-quadratic growth is {Gotts dots}.
See also {Fermat prime calculator}.
:initials: = {monogram}
:inline inverter: The following reaction in which a p30 {gun} can be
used to invert the presence or absence of gliders in a p30 stream,
with the output glider stream being in the same direction as the
input glider stream.
................*...................
.................*..................
...............***..................
....................................
.......................*.*..........
.....................*...*..........
.............*.......*..............
............****....*....*........**
...........**.*.*....*............**
**........***.*..*...*...*..........
**.........**.*.*......*.*..........
............****....................
.............*......................
:integral: = {integral sign}
:integral sign: (p1)
...**
..*.*
..*..
*.*..
**...
:intentionless: = {elevener}
:interchange: (p2) A common formation of six blinkers.
..***....***..
..............
*............*
*............*
*............*
..............
..***....***..
:intermediate target: A temporary product of a partial {slow salvo},
{elbow operation}, or {glider synthesis}. An intermediate target is
a useful step toward a desired outcome, but will not appear in the
final construction.
:intermitting glider gun: Despite the name, an intermitting glider gun
(IMG) is more often an {oscillator} than a {gun}. There are two
basic types. A type 1 IMG consists of two guns firing at one another
in such a way that each gun is temporarily disabled on being hit by a
glider from the other gun. A type 2 IMG consists of a single gun
firing at a 180-degree glider {reflector} in such a way that
returning gliders temporarily disable the gun.
Both types of IMG can be used to make glider guns of periods that
are multiples of the base period. This is done by firing another gun
across the two-way intermittent glider stream of the IMG in such a
way that gliders only occasionally escape.
:island: The individual {polyplet}s of which a {stable} pattern
consists are sometimes called islands. So, for example, a {boat} has
only one island, while an {aircraft carrier} has two, a {honey farm}
has four and the standard form of the {eater3} has five.
:Iwona: (stabilizes at time 28786) The following {methuselah} found by
Andrzej Okrasinski in August 2004.
..............***...
....................
....................
....................
....................
....................
..*.................
...**...............
...*..............*.
..................*.
..................*.
...................*
..................**
.......**...........
........*...........
....................
....................
....................
....................
**..................
.*..................
:J: = {Herschel}
:jack: (p4) Found by Robert Wainwright, April 1984.
...*.....*...
...**...**...
*..**...**..*
***..*.*..***
.....*.*.....
***..*.*..***
*..**...**..*
...**...**...
...*.....*...
:jagged lines: A pattern constructed by Dean Hickerson in May 2005 that
uses {puffer}s to produce a line of {bi-block}s that weaves back and
forth in a complicated way.
:jam: (p3) Found by Achim Flammenkamp in 1988, but not widely known
about until its independent discovery (and naming) by Dean Hickerson
in September 1989. Compare with {mold}. In fact this is really very
like {caterer}. In terms of its 7x7 {bounding box} it ties with
{trice tongs} as the smallest p3 {oscillator}.
...**.
..*..*
*..*.*
*...*.
*.....
...*..
.**...
:JavaLifeSearch: See {lifesrc}.
:Jaws: A {breeder} constructed by Nick Gotts in February 1997. In the
original version Jaws had an initial {population} of 150, which at
the time was the smallest for any known pattern with superlinear
growth. In November 1997 Gotts produced a 130-cell Jaws using some
{switch engine} {predecessor}s found by Paul Callahan. Jaws has
since been beaten by the even smaller {mosquito}es, {teeth},
{catacryst}, {metacatacryst}, {Gotts dots} and {wedge}.
Jaws consists of eight pairs of switch engines which produce a new
block-laying switch engine (plus masses of junk) every 10752
generations. It is therefore an MMS breeder.
:JC: = {dead spark coil}
:JHC: John Horton Conway. Also another name for {monogram}.
:J-heptomino: = {Herschel}
:JLS: = {JavaLifeSearch}
:Jolson: (p15) Two {block}s {hassle}d by two {pentadecathlon}s. Found
by Robert Wainwright in November 1984 and named by Bill Gosper. A p9
version using {snacker}s instead of pentadecathlons is also possible.
.**......**..
*..*....*..*.
*..*....*..*.
*..*....*..*.
.**......**..
.............
.............
.......*.....
.....*..*.**.
......**..**.
.............
.............
......****...
.....******..
....********.
...**......**
....********.
.....******..
......****...
:Justyna: (stabilizes at time 26458) The following {methuselah} found
by Andrzej Okrasinski in May 2004.
.................*....
................*..*..
.................***..
.................*..*.
......................
**................*...
.*................*...
..................*...
......................
......................
......................
......................
......................
......................
......................
...................***
...........***........
:keys: See {short keys}, {bent keys} and {odd keys}.
:kickback: + See also {180-degree kickback}.
:kickback reaction: The following collision of two {glider}s whose
product is a single glider travelling in the opposite direction to
one of the original gliders. This is important in the proof of the
existence of a {universal constructor}, and in Bill Gosper's {total
aperiodic}, as well as a number of other constructions.
.....*..
......**
.**..**.
*.*.....
..*.....
See also {180-degree kickback}.
:kidney: A Gosperism for {century}. See also {diuresis}.
:killer toads: A pair of {toad}s acting together so that they can eat
things. Here, for example, are some killer toads eating a {HWSS}.
Similarly they can eat a {MWSS} (but not a {LWSS}). For another
example see {twirling T-tetsons II}. See also {candlefrobra}.
..**.......***
*....*....***.
......*.......
*.....*.......
.******.......
..........***.
...........***
:Klein bottle: As an alternative to a {torus}, it's possible to make a
finite Life universe in the form of a Klein bottle. The simplest way
to do this is to use an m x n rectangle with the top edge joined to
the bottom edge (as for a torus) and the left edge twisted and joined
to the right.
:knightship: Any {spaceship} of type (2m,m)/n -- that is, a spaceship
of any speed that moves obliquely in a (2,1) direction. The first
Conway's Life knightship was a variant of Andrew Wade's {Gemini}
spaceship, constructed in May 2010. The next was an even slower
knightship based on the {half-bakery reaction}. A knightship must be
asymmetric and its period must be at least 6, which makes it very
difficult to search for {elementary} knightships using programs like
{lifesrc}.
By analogy with the corresponding fairy chess pieces, spaceships of
types (3m,m)/n, (3m,2m)/n and (4m,m)/n would presumably be called
camelships, zebraships and giraffeships, respectively. Such
spaceships do exist (see {universal constructor}) but small
elementary versions are even more difficult to search for. No
concrete example has been constructed, though this could be done
trivially by modifying a Gemini spaceship, or less trivially by
reprogramming one of the more recent small {Geminoid} {construction
arm}s.
:Kok's galaxy: (p8) Found by Jan Kok in 1971. See {converter} for a
use of this {sparker}.
******.**
******.**
.......**
**.....**
**.....**
**.....**
**.......
**.******
**.******
:L112: A {composite conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Dave Buckingham in July 1996. It is made up
of two {elementary conduit}s, HLx53B + {BFx59H}. After 112 ticks,
it produces a {Herschel} turned 90 degrees counterclockwise at (12,
-33) relative to the input. Its {recovery time} is 61 ticks; this
can be reduced slightly by removing the output glider, either with a
specialized eater (as in the original {true} p59 gun), or with a
{sparker} as in most of the {Quetzal} guns. It can be made {Spartan}
by replacing the {aircraft carrier} with an eater1 in one of two
orientations. A {ghost Herschel} in the pattern below marks the
output location:
...............**.......
...............*........
.............***........
........................
........................
........................
........................
........................
........................
........................
........................
........................
........................
........................
........................
........................
........................
........................
.............**.........
.............**.........
....**..................
....*..*................
**....**................
.*....................**
.*.*..................*.
..**................*.*.
....................**..
........................
........................
........................
........................
........................
..*.....................
..*.*...................
..***...................
....*...................
........................
..............**........
..............**..**....
..................*.*...
....................*...
....................**..
:L156: A {composite conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Dave Buckingham in August 1996. It is made
up of three {elementary conduit}s, HLx69R + RF28B + {BFx59H}. After
156 ticks, it produces a {Herschel} turned 90 degrees
counterclockwise at (17, -41) relative to the input. Its {recovery
time} is 62 ticks. It can be made {Spartan} by replacing the {snake}
with an {eater1} in one of two orientations. A {ghost Herschel} in
the pattern below marks the output location:
...................**........
...................*.........
.................***.........
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.............................
.................**..........
.................**..........
.............................
........**.*.................
........*.**.................
..........................**.
..........................*..
........................*.*..
........................**...
.............................
.........*...................
.........***.................
*...........*................
***........**..............*.
...*......................*.*
..**.......................*.
.............................
.............................
.............................
.............................
.............................
.............................
.*....................**.....
.*.*..................*.*....
.***....................*....
...*...........**.......**...
...............*.............
................***..........
..................*..........
:lake: Any still life consisting of a simple closed curve made from
diagonally connected {domino}es. The smallest example is the {pond},
and the next smallest is this (to which the term is sometimes
restricted):
....**....
...*..*...
...*..*...
.**....**.
*........*
*........*
.**....**.
...*..*...
...*..*...
....**....
:lane: a path traveled by a glider, or less commonly, a spaceship such
as a loafer. The lane is centered on the line of symmetry (if any)
of the spaceship in question. If a lane is clear, then the spaceship
can travel along it without colliding or interfering with any other
objects.
Diagonal lanes are often numbered consecutively, in half-diagonals
({hd}). Occasionally diagonal lane measurements are given in
quarter-diagonals ({qd}), in part because diagonally symmetric
spaceships have a line of symmetry 1qd away from the lines available
for gliders. It's also convenient that moving a glider forward by
100qd (for example) has the same effect as evolving the same glider
for 100 ticks.
:Laputa: (p2) Found by Rich Schroeppel, September 1992.
...**.**....
...**.*...**
........*..*
.******.***.
*..*.*......
**...*.**...
....**.**...
:large S: = {big S}
:Lidka: (stabilizes at time 29053) A {methuselah} found by Andrzej
Okrasinski in July 2005.
..........***..
..........*....
..........*...*
...........*..*
............***
...............
.*.............
*.*............
.*.............
The following variant, pointed out by David Bell, has two fewer cells
and lasts two generations longer.
..........***..
...............
...........**.*
............*.*
..............*
...............
.*.............
*.*............
.*.............
:Life: A 2-dimensional 2-state {cellular automaton} discovered by John
Conway in 1970. The states are referred to as ON and OFF (or live
and dead). The transition rule is as follows: a cell that is ON will
remain ON in the next generation if and only if exactly 2 or 3 of the
8 adjacent cells are also ON, and a cell that is OFF will turn ON if
and only if exactly 3 of the 8 adjacent cells are ON. (This is more
succinctly stated as: "If 2 of your 8 nearest neighbours are ON,
don't change. If 3 are ON, turn ON. Otherwise, turn OFF.")
:Life32: A freeware Life program by Johan Bontes for Microsoft Windows
95/98/ME/NT/2000/XP: {https://github.com/JBontes/Life32/}.
:LifeHistory: A multistate CA rule equivalent to two-state B3/S23 Life,
but with several additional states intended for annotation purposes.
A "history" state records whether an off cell has ever turned on in
the past, and other states allow on and off cells to be permanently
or temporarily marked, without affecting the evolution of the
pattern.
:LifeLab: A shareware Life program by Andrew Trevorrow for the
Macintosh (MacOS 8.6 or later): {http://www.trevorrow.com/lifelab/}.
:LifeLine: A newsletter edited by Robert Wainwright from 1971 to 1973.
During this period it was the main forum for discussions about Life.
The newsletter was nominally quarterly, but the actual dates of its
eleven issues were as follows:
Mar, Jun, Sep, Dec 1971
Sep, Oct, Nov, Dec 1972
Mar, Jun, Sep 1973
:Lifenthusiast: A Life enthusiast. Term coined by Robert Wainwright.
:lifesrc: David Bell's Life search program, for finding new
{spaceship}s and {oscillator}s. This is a C implementation of an
algorithm developed by Dean Hickerson in 6502 assembler. Most of the
spaceships and many of the oscillators shown in this lexicon were
found with lifesrc or by Hickerson's original program.
Although lifesrc itself is a command-line program, Jason Summers
has made a GUI version called {WinLifeSearch} for Microsoft Windows.
A Java version, {JavaLifeSearch}, was written in November 2012 by
Karel Suhajda.
The lifesrc algorithm is only useful for very small periods, as the
amount of computing power required rises rapidly with increasing
period. For most purposes, period 7 is the practical limit with
current hardware.
Lifesrc is available from {http://www.canb.auug.org.au/~dbell/}
(source code only).
Compare {gfind}.
:LifeViewer: A scriptable Javascript Life pattern viewer written by
Chris Rowett, used primarily on the conwaylife.com discussion forums.
:light bulb: (p2) Found in 1971.
.**.*..
.*.**..
.......
..***..
.*...*.
.*...*.
..*.*..
*.*.*.*
**...**
The same {rotor} can be embedded in a slightly smaller {stator} like
this:
...*.....
.***.....
*........
******...
......*..
..*...*..
..**.*...
......***
........*
:lightspeed bubble: A type of {negative spaceship} traveling through
the {zebra stripes} agar. The center of the bubble is simple empty
space, and the length and/or width of the bubble can usually be
extended to any desired size.
Below is a small stabilized section of agar containing a sample
lightspeed bubble, found by Gabriel Nivasch in August 1999. The
bubble travels to the left at {the speed of light}, so it will
eventually reach the edge of any finite patch and destroy itself and
its supporting agar.
.*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*...
.************************************************************.
.............................................................*
.*************..***..***..***********************************.
*..............**...**...**........*..........................
.*************...**...**...*.**.*....************************.
.............................**.....*........................*
.*************.................******************************.
*...............................*.............................
.*************...................****************************.
.................................*....*......................*
.*************...................**....**********************.
*................................*.....*....*.................
.*************...................**....**....****************.
.................................*.....*.....*....*..........*
.*************...................**....**....**....**********.
*................................*.....*.....*.....*....*.....
.*************...................**....**....**....**....****.
.................................*.....*.....*.....*.....*...*
.*************...................**....**....**....**....****.
*................................*.....*.....*.....*....*.....
.*************...................**....**....**....**********.
.................................*.....*.....*....*..........*
.*************...................**....**....****************.
*................................*.....*....*.................
.*************...................**....**********************.
.................................*....*......................*
.*************...................****************************.
*...............................*.............................
.*************.................******************************.
.............................**.....*........................*
.*************...**...**...*.**.*....************************.
*..............**...**...**........*..........................
.*************..***..***..***********************************.
.............................................................*
.************************************************************.
.*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*...
An open problem related to lightspeed bubbles was whether large
extensible empty areas could be created whose length was not
proportional to the width (as it must be in the above case, due to
the tapering back edge). This was solved in February 2017 by Arie
Paap; a simple period-2 solution is shown below.
...*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*...
.***********************************************************.
*...........................................................*
.***********************************************************.
.............................................................
.***********************************************************.
*.....................................................*.....*
.********************..***..***..***..********..****...*****.
......................**...**...**...**........**.....*......
.********************...**...**...**...*******...*.**..*****.
*.........................................*........**.......*
.********************......................**.*......*******.
...........................................*............*....
.********************......................*.............***.
*..........................................**.....**....*...*
.********************......................**...**...*.*****.
...........................................*..*.**...*.......
.********************......................*......**...*****.
*..........................................**..........*....*
.********************......................**..........*****.
...........................................*......**.*.......
.********************......................*..*.**...*.*****.
*..........................................**...**......*...*
.********************......................**.....**.....***.
...........................................*............*....
.********************......................*...........*****.
*..........................................**.....**.**.....*
.********************......................**...**...**..***.
...........................................*..*.**.....**....
.********************......................*......**....****.
*..........................................**...............*
.********************......................**...........****.
...........................................*......**...**....
.********************......................*..*.**...**..***.
*..........................................**...**...**.....*
.********************......................**.....**...*****.
...........................................*............*....
.**********************.....*.....*.....*..*.*...........***.
*.........................**....**....**...*...*.*.......*..*
.************************.**.**.**.**.**.*********.......***.
........................................................*....
.*************************************************...*******.
*..................................................**.......*
.*************************************************..********.
.............................................................
.***********************************************************.
*...........................................................*
.***********************************************************.
...*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*...
:lightspeed ribbon: = {superstring}
:lightspeed telegraph: = {telegraph}.
:lightspeed wire: Any {wick} that can burn non-destructively at the
speed of light. These are potentially useful for various things,but
so far the necessary mechanisms are very large and unwieldy. In
October 2002, Jason Summers discovered a lightspeed reaction
traveling through an orthogonal chain of beehives:
Summers completed a period-1440 lightspeed {telegraph} based on this
reaction in 2003.
...*...........................................................
.*...*.........................................................
.*....*....**.**...............................................
*......*...******...**...**...**...**...**...**...**...**...**.
*......*..*......*.*..*.*..*.*..*.*..*.*..*.*..*.*..*.*..*.*..*
**.....*...******...**...**...**...**...**...**...**...**...**.
......*....**.**...............................................
....*..........................................................
A {stable} lightspeed {transceiver} mechanism using this same
signal reaction, the {p1 telegraph}, was constructed by Adam P.
Goucher in 2010; the bounding boxes of both the {transmitter} and
{receiver} are over 5000 cells on a side. A more compact periodic
{high-bandwidth telegraph} with a much improved transmission rate was
completed by Jean-Francois Handfield in 2017.
The following diagram shows an older example of a lightspeed wire,
with a small defect that travels along it at the speed of light. As
of this writing (August 2017) no method has been found of creating
such a defect in the upstream end of this particular stable wire, or
of non-destructively detecting the arrival of the defect and
repairing the wire at the downstream end.
....**..**..**..**..**..**..**..**..**..**..**..**..**....
....**..**..**..**..**..**..**..**..**..**..**..**..**....
..........................................................
..******************************************************..
.*......*...............................................*.
*.*****....*********************************************.*
.*.....*................................................*.
..******************************************************..
..........................................................
....**..**..**..**..**..**..**..**..**..**..**..**..**....
....**..**..**..**..**..**..**..**..**..**..**..**..**....
:lightweight emulator: = {LW emulator}
:lightweight spaceship: = {LWSS}
:lightweight volcano: = {toaster}
:linear growth: A growth rate proportional to T, where T is the number
of ticks that a pattern has been run. Compare {superlinear growth},
{quadratic growth}.
:linear propagator: a self-replicating pattern in which each copy of a
pattern produces one child that is an exact copy of itself. The
child pattern then blocks the parent from any further replication.
An example was constructed by Dave Greene on 23 November 2013, with a
construction arm using two glider lanes separated by {9hd}. By some
definitions, due to its limited one-dimensional growth pattern, the
linear propagator is not a true replicator, Compare {quadratic
replicator}.
:line-cutting reaction: A reaction that can cut an infinite diagonal
line of cells, leaving a gap with both ends sealed.
:line puffer: A {puffer} which produces its output by means of an
orthogonal line of cells at right angles to the direction of travel.
The archetypal line puffer was found by Alan Hensel in March 1994,
based on a {spaceship} found earlier that month by Hartmut Holzwart.
The following month Holzwart found a way to make {extensible} c/2
line puffers, and Hensel found a much smaller stabilization the
following day. But in October 1995 Tim Coe discovered that for large
widths these were often unstable, although typically lasting millions
of generations. In May 1996, however, Coe found a way to fix the
instability. The resulting puffers appear to be completely stable
and to exhibit an exponential increase in period as a function of
width, although neither of these things has been proved.
Line puffers have enabled the construction of various difficult
periods for c/2 spaceships and puffers, including occasionally
periods which are not multiples of 4 and which would therefore be
impossible to attain with the usual type of construction based on
{standard spaceship}s. (See {frothing puffer} for another method of
constructing such periods.) In particular, the first c/2 {rake} with
period not divisible by 4 was achieved in January 2000 when David
Bell constructed a p42 {backrake} by means of line puffers.
See also {hivenudger} and {puff suppressor}.
:line ship: A {spaceship} in which the front end is a {linestretcher},
the line being eaten by the back end.
:linestretcher: A {wickstretcher} that stretches a single diagonal line
of cells. The first example was constructed by Jason Summers in
March 1999; this was c/12 and used {switch engine} based puffers
found earlier by Dean Hickerson. The first c/4 example was found by
Hartmut Holzwart in November 2004.
:loading dock: (p3) Found by Dave Buckingham, September 1972.
....*....
..***....
.*...**..
*.**...*.
.*...**.*
..**...*.
....***..
....*....
:loaf: (p1)
.**.
*..*
.*.*
..*.
:loafer: (c/7 orthogonally, p7) A small {c/7 spaceship} discovered by
Josh Ball on 17 February 2013:
.**..*.**
*..*..**.
.*.*.....
..*......
........*
......***
.....*...
......*..
.......**
It has a known 8-glider construction recipe, probably not minimal,
discovered on the following day:
.................................*
...............................**.
................................**
.........*........................
.*........*.......................
..*.....***.......................
***...............................
..................................
..................................
.....*............................
......*...........................
....***...........................
........................*.*.......
.........................**.......
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..................................
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...........................**.....
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...............................***
...............................*..
................................*.
..................................
..................................
..................................
..................................
..................................
..................................
.....**...........................
......**..........................
.....*............................
The loafer was therefore the first new glider-constructible spaceship
in almost a decade. (A {glider synthesis} for a 2c/5 ship,
{60P5H2V0}, was found in March 2003.)
:loaflipflop: (p15) Here four {pentadecathlon}s {hassle} a {loaf}.
Found by Robert Wainwright in 1990.
................*.................
...............***................
..................................
..................................
...............***................
..................................
...............*.*................
...............*.*................
..................................
...............***................
..................................
..................................
...............***................
................*.................
..................................
.*..*.**.*..*...............**....
**..*....*..**...**.......*....*..
.*..*.**.*..*...*..*.....*......*.
................*.*.....*........*
.................*......*........*
........................*........*
.........................*......*.
..........................*....*..
............................**....
..................***.............
.................*...*............
................*.....*...........
..................................
...............*.......*..........
...............*.......*..........
..................................
................*.....*...........
.................*...*............
..................***.............
:loaf on loaf: = {bi-loaf}
:loaf pull: The following glider/loaf collision, which pulls a loaf
(3,1) toward the glider source:
.*.....
*.*....
*..*...
.**....
.......
.......
....***
....*..
.....*.
:loaf siamese barge: (p1)
..**.
.*..*
*.*.*
.*.*.
..*..
:lobster: (c/7 diagonally, p7) A spaceship discovered by Matthias
Merzenich in August 2011, the first diagonally traveling {c/7
spaceship} to be found. It consists of two {glider}s pulling a
{tagalong} that then rephases them.
............***...........
............*.............
.............*..**........
................**........
............**............
.............**...........
............*..*..........
..........................
..............*..*........
..............*...*.......
...............***.*......
....................*.....
**..*.*.............*.....
*.*.**.............*......
*....*..**.............**.
......*...*......**..**..*
..**......*......*..*.....
..**....*.*....**.........
.........*.....*...*...*..
..........*..*....**......
...........**...*.....*.*.
...............*........**
...............*....*.....
..............*...*.......
..............*.....**....
...............*.....*....
:LoM: = {lumps of muck}
:lone dot agar: An {agar} in which every live cell is isolated in every
generation.
:lonely bee: = {worker bee}
:long: A term applied to an object that is of the same basic form as
some standard object, but longer. For examples see {long barge},
{long boat}, {long bookend}, {long canoe}, {long shillelagh}, {long
ship} and {long snake}.
:long^3: The next degree of longness after {long long}. Some people
prefer "extra long".
:long^4: The next degree of longness after {long^3}. Some people
prefer "extra extra long".
:long barge: (p1)
.*...
*.*..
.*.*.
..*.*
...*.
:long boat: (p1)
.*..
*.*.
.*.*
..**
:long bookend: The following {induction coil}, longer than a {bookend}.
...**
*...*
****.
:long canoe: (p1)
....**
.....*
....*.
...*..
*.*...
**....
:long hat: = {loop}
:long hook: = {long bookend}
:long house: = {dock}
:long integral: (p1)
..**
.*.*
.*..
..*.
*.*.
**..
:long long: The next degree of longness after {long}. Some people
prefer "very long".
:long long barge: (p1)
.*....
*.*...
.*.*..
..*.*.
...*.*
....*.
:long long boat: (p1)
.*...
*.*..
.*.*.
..*.*
...**
:long long canoe: (p1)
.....**
......*
.....*.
....*..
...*...
*.*....
**.....
:long long ship: (p1)
**...
*.*..
.*.*.
..*.*
...**
:long long snake: (p1)
**....
*.*...
...*.*
....**
:long shillelagh: (p1)
**..**
*..*.*
.**...
:long ship: (p1)
**..
*.*.
.*.*
..**
:long sinking ship: = {long canoe}
:long snake: (p1)
**...
*.*.*
...**
:loop: (p1)
.**..
*..*.
.*.*.
**.**
:low-density Life: = {sparse Life}
:lumps of muck: The common evolutionary sequence that ends in the
{blockade}. The name is sometimes used of the blockade itself, and
can in general be used of any stage of the evolution of the
{stairstep hexomino}.
:LW emulator: (p4) The smallest (and least useful) {emulator}, found by
Robert Wainwright in June 1980.
..**.*..*.**..
..*........*..
...**....**...
***..****..***
*..*......*..*
.**........**.
:LWSS: (c/2 orthogonally, p4) A lightweight spaceship, the smallest
known orthogonally moving {spaceship}, and the second most common
(after the {glider}). Found by Conway when one formed from a random
soup in 1970. See also {MWSS} and {HWSS}.
.*..*
*....
*...*
****
:LWSS emulator: = {LW emulator}
:LWSS-to-G: See {135-degree MWSS-to-G}.
:LWTDS: Life Worker Time Deficiency Syndrome. Term coined by Dieter
Leithner to describe the problem of having to divide scarce time
between Life and real life.
:LW volcano: = {toaster}
:Lx200: A {composite conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Paul Callahan in June 1997. It is made up
of two {elementary conduit}s, HL141B + {BFx59H}. The Lx200 and {F166}
conduits are the two original {dependent conduit}s (several more have
since been discovered.) After 200 ticks, it produces an inverted
{Herschel} turned 90 degrees counterclockwise at (17, -40) relative
to the input. Its {recovery time} is 90 ticks. It can be made
{Spartan} by replacing the {snake}s with {eater1}s in one of two
orientations. A {ghost Herschel} in the pattern below marks the
output location:
.....................**.............
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..............**.*..................
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................................*.*.
.**...............................*.
***.**............................**
.**.***.**..........................
***.**..**..........................
**..................................
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................................**..
................................**..
....................................
......**............................
.......*............................
....***.........................**..
....*...........................**..
..................**................
.................*.*................
.................*..................
................**........**........
..........................*.........
...........................***......
.............................*......
The input shown here is a {Herschel great-grandparent}, since the
input reaction is catalysed by the {transparent} block before the
Herschel's standard form can appear.
:macro-spaceship: A {self-constructing} or {self-supporting} spaceship,
such as the {Caterpillar}, {Centipede}, {half-baked knightship},
{waterbear}, {Demonoid}, {Orthogonoid}, and {Caterloopillar}.
Engineered spaceships of these types are inevitably large and
complex.
:mango: (p1)
.**..
*..*.
.*..*
..**.
:mathematician: (p5) Found by Dave Buckingham, 1972.
....*....
...*.*...
...*.*...
..**.**..
*.......*
***...***
.........
*********
*.......*
...****..
...*..**.
:Max: A name for the smallest known {spacefiller}. The name represents
the fact that the growth rate is the fastest possible. (This has not
quite been proved, however. There remains the possibility, albeit
not very likely, that a periodic {agar} could have an average
{density} greater than 1/2, and a spacefiller stretching such an agar
at the same speed as the known spacefillers would have a faster
average growth rate.)
:mazing: (p4) In terms of its minimum {population} of 12 this ties with
{mold} as the smallest p4 {oscillator}. Found by Dave Buckingham in
December 1973. For some constructions using mazings, see {popover}
and {sixty-nine}.
...**..
.*.*...
*.....*
.*...**
.......
...*.*.
....*..
:medium fish: = {MWSS}
:megacell: = {p1 megacell}.
:metacatacryst: A 52-cell pattern exhibiting quadratic growth. Found
by Nick Gotts, December 2000. This was for some time the smallest
known pattern (in terms of initial population) with superlinear
growth. See also {catacryst} for more recent record-holders.
:metacell: CA logic circuitry that emulates the behavior of a single
cell. The circuitry is hard-wired to emulate a particular CA rule,
but changing the rule is usually a matter of making simple
adjustments. Known examples include David Bell's original 500x500
{unit cell}, Jared Prince's {Deep Cell}, Brice Due's {OTCA
metapixel}, and Adam P. Goucher's {megacell}.
:metamorphosis: An {oscillator} built by Robert Wainwright that uses
the following reaction (found by Bill Gosper) to turn {glider}s into
{LWSS}, and converts these LWSS back into gliders by colliding them
head on. (There are in fact two ways to do the following reaction,
because the {spark} of the {twin bees shuttle} is symmetric.)
...................*.........
....................*........
..................***........
.............................
.............................
.............................
.............................
.............................
............*...*.....*.**...
**.........*.....*....*.*.*..
**.........*.........*....*..
...........**...*.....*.*.*..
.............***......*.**...
.............................
.............***.............
...........**...*............
**.........*...............**
**.........*.....*.........**
............*...*............
:metamorphosis II: An oscillator built by Robert Wainwright in December
1994 based on the following p30 {glider}-to-{LWSS} {converter}. This
converter was first found by Paul Rendell, January 1986 or earlier,
but wasn't widely known about until Paul Callahan rediscovered it in
December 1994.
......................*.
.....................*..
.....................***
........................
........................
.........*.*............
.........*..*...........
**..........**..........
**........*...**........
.....**.....**..........
....*....*..*...........
.........*.*............
........................
........................
........................
........................
................*.......
...............***......
..............*****.....
.............*.*.*.*....
.............**...**....
........................
........................
................*.......
...............*.*......
...............*.*......
................*.......
...............**.......
...............**.......
...............**.......
:metapixel: See {metacell}, {OTCA metapixel}.
:methuselah: Any small pattern that stabilizes only after a long time.
Term coined by Conway. Examples include {rabbits}, {acorn}, the
{R-pentomino}, {blom}, {Iwona}, {Justyna} and {Lidka}. See also
{ark}.
:Mickey Mouse: (p1) A name proposed by Mark Niemiec for the following
{still life}:
.**....**.
*..*..*..*
*..****..*
.**....**.
...****...
...*..*...
....**....
:middleweight emulator: = {MW emulator}
:middleweight spaceship: = {MWSS}
:middleweight volcano: = {MW volcano}
:mini pressure cooker: (p3) Found by Robert Wainwright before June
1972. Compare {pressure cooker}.
.....*.....
....*.*....
....*.*....
...**.**...
*.*.....*.*
**.*.*.*.**
...*...*...
...*.*.*...
....*.*....
.....*.....
:M.I.P. value: The maximum {population} divided by the initial
population for an unstable pattern. For example, the {R-pentomino}
has an M.I.P. value of 63.8, since its maximum population is 319.
The term is no longer in use.
:MIT oscillator: = {cuphook}
:MMM breeder: See {breeder}.
:MMS breeder: See {breeder}.
:mod: The smallest number of generations it takes for an {oscillator}
or {spaceship} to reappear in its original form, possibly subject to
some rotation or reflection. The mod may be equal to the {period},
but it may also be a quarter of the period (for oscillators that
rotate 90 degrees every quarter period) or half the period (for other
oscillators which rotate 180 degrees every half period, and also for
{flipper}s).
:mold: (p4) Found by Achim Flammenkamp in 1988, but not widely known
until Dean Hickerson rediscovered it (and named it) in August 1989.
Compare with {jam}. In terms of its minimum {population} of 12 it
ties with {mazing} as the smallest p4 {oscillator}. But in terms of
its 6x6 {bounding box} it wins outright. In fact, of all oscillators
that fit in a 6x7 box it is the only one with {period} greater than
2.
...**.
..*..*
*..*.*
....*.
*.**..
.*....
:monochromatic salvo: A {slow salvo} that uses gliders of only one
colour. For example, the slow salvos generated by {half-baked
knightship}s are monochromatic, because they are generated by a
single type of reaction which can happen at any position along a
diagonal line. The smallest possible step size is one {full
diagonal} (1fd), which is two {half diagonal}s (2hd), which means
that any single glider-producing reaction can only reach half of the
available glider {lane}s. See {colour of a glider}.
:monogram: (p4) Found by Dean Hickerson, August 1989.
**...**
.*.*.*.
.**.**.
.*.*.*.
**...**
:monoparity salvo: A {slow salvo} that uses gliders of only one
{parity}. Compare {monochromatic salvo}.
:Moore neighbourhood: The set of all cells that are orthogonally or
diagonally adjacent to a cell or group of cells. The von Neumann
neighbourhood of a cell can be thought of as the points at a
Chebyshev distance of 1 from that cell. Compare {von Neumann
neighbourhood}. The Conway's Life rule is based on the Moore
neighborhood, as are all the "Life-like" rules and many other
commonly investigated rule families.
Cell neighbourhoods can also be defined with a higher range. The
Moore neighbourhood of range n can be defined recursively as the
Moore neighbourhood of the Moore neighbourhood of range n-1. For
example, the Moore neighbourhood of range 2 includes all cells that
are orthogonally or diagonally adjacent to the standard Moore
neighbourhood.
:moose antlers: (p1)
**.....**
*.......*
.***.***.
...*.*...
....*....
:mosquito: See {mosquito1}, {mosquito2}. {mosquito3}, {mosquito4} and
{mosquito5}.
:mosquito1: A {breeder} constructed by Nick Gotts in September 1998.
The original version had an initial population of 103, which was then
the smallest for any known pattern with superlinear growth (beating
the record previously held by {Jaws}). This was reduced to 97 by
Stephen Silver the following month, but was then almost immediately
superseded by {mosquito2}.
Mosquito1 consists of the classic {puffer train} plus four {LWSS}
and four {MWSS} (mostly in {predecessor} form, to keep the population
down). Once it gets going it produces a new block-laying {switch
engine} (plus a lot of junk) every 280 generations. It is therefore
an MMS breeder, albeit a messy one.
:mosquito2: A {breeder} constructed by Nick Gotts in October 1998. Its
initial population of 85 was for a couple of hours the smallest for
any known pattern with superlinear growth, but was then beaten by
{mosquito3}.
Mosquito2 is very like {mosquito1}, but uses two fewer {MWSS} and
one more {LWSS}.
:mosquito3: A {breeder} constructed by Nick Gotts in October 1998. Its
initial population of 75 was at the time the smallest for any known
pattern with superlinear growth, but was beaten a few days later by
{mosquito4}.
Mosquito3 has one less {LWSS} than {mosquito2}. It is somewhat
different from the earlier mosquitoes in that the {switch engine}s it
makes are glider-producing rather than block-laying.
:mosquito4: A slightly improved version of {mosquito3} which Stephen
Silver produced in October 1998 making use of another discovery of
Nick Gotts (September 1997): an 8-cell pattern that evolves into a
{LWSS} plus some junk. Mosquito4 is a {breeder} with an initial
population of 73, at the time the smallest for any known pattern with
superlinear growth, but superseded a few days later by {mosquito5}.
:mosquito5: A slightly improved version of {mosquito4} which Nick Gotts
produced in October 1998. The improvement is of a similar nature to
the improvement of mosquito4 over mosquito3. Mosquito5 is a
{breeder} with an initial population of 71. At the time, this was
the smallest population for any known pattern with superlinear
growth, but it has since been superseded by {teeth}, {catacryst},
{metacatacryst}, {Gotts dots} and {wedge}.
:mould: = {mold}
:moving sawtooth: A {sawtooth} such that no cell is ON for more than a
finite number generations. David Bell has constructed patterns of
this type, with a c/2 front end and a c/3 back end.
:MSM breeder: See {breeder}.
:multi-state Life: = {colorized Life}
:multum in parvo: (stabilizes at time 3933) A {methuselah} found by
Charles Corderman, but not as long-lasting as his {acorn}.
...***
..*..*
.*....
*.....
:muttering moat: Any {oscillator} whose {rotor} consists of a closed
chain of cells each of which is adjacent to exactly two other rotor
cells. Compare {babbling brook}. Examples include the {bipole}, the
{blinker}, the {clock}, the {cuphook}, the {Gray counter}, the
{quad}, the {scrubber}, the {skewed quad} and the p2 {snake pit}. The
following diagram shows a p2 example (by Dean Hickerson, May 1993)
with a larger rotor. See {ring of fire} for a very large one.
**.....
*.*.**.
.....*.
.*..*..
..*....
..*.*.*
.....**
:MW emulator: (p4) Found by Robert Wainwright in June 1980. See also
{emulator} and {filter}.
.......*.......
..**.*...*.**..
..*.........*..
...**.....**...
***..*****..***
*..*.......*..*
.**.........**.
:MWSS: (c/2 orthogonally, p4) A middleweight spaceship, the third most
common {spaceship}. Found by Conway in 1970 by modifying a {LWSS}.
See also {HWSS}.
...*..
.*...*
*.....
*....*
*****.
:MWSS emulator: = {MW emulator}
:MWSS out of the blue: The following reaction, found by Peter Rott in
November 1997, in which a {LWSS} passing by a p46 {oscillator}
creates a {MWSS} travelling in the opposite direction. Together with
some reactions found by Dieter Leithner, and a LWSS-turning reaction
which Rott had found in November 1993 (but which was not widely known
until Paul Callahan rediscovered it in June 1994) this can be used to
prove that there exist {gliderless} guns for LWSS, MWSS and {HWSS}
for every period that is a multiple of 46.
*..*.................................
....*................................
*...*................................
.****................................
.....................................
.....................................
.....................................
.....................................
.....................................
...................**..............**
..................**...............**
...................*****.............
..**................****.............
..**.....*...........................
........***.........****.............
.......*.*.*.......*****.............
........*..*......**...............**
........***........**..............**
.........*...........................
.....................................
.....................................
.....................................
.....................................
..*.......*..........................
.....................................
***.......***........................
.**.**.**.**.........................
..***...***..........................
...*.....*...........................
.....................................
.....................................
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.....................................
.....................................
.....................................
..**.....**..........................
..**.....**..........................
:MWSS-to-G: See {135-degree MWSS-to-G}, {45-degree MWSS-to-G}.
:MW volcano: (p5) Found by Dean Hickerson in April 1992.
......*......
....*...*....
.............
...*.....*...
.***.***.***.
*...**.**...*
*.***.*.****.
.*...........
...*.*.*.**.*
..**.***.*.**
...*.*..*....
...*..**.....
..**.........
:My Experience with B-heptominos in Oscillators: An article by Dave
Buckingham (October 1996) that describes his discovery of {Herschel
conduit}s, including sufficient (indeed ample) {stable} conduits to
enable, for the first time, the construction of period n oscillators
- and true period n guns - for every sufficiently large integer n.
(See {Herschel loop} and {emu}.)
:natural: Occurring often in random patterns. There is no precise
measure of naturalness, since the most useful definition of "random"
in this context is open to debate. Nonetheless, it is clear that
objects such as {block}s, {blinker}s, {beehive}s and {glider}s are
very natural, while {eater2}s, {dart}s, {gun}s, etc., are not.
:negative spaceship: a type of {signal} traveling through a periodic
{agar} such as {zebra stripes}. The leading edge of the signal
removes the agar, and the trailing edge rebuilds the agar some time
later. The distance between the two edges is sometimes adjustable --
see {lightspeed bubble}. The central part of the "spaceship" may
consist of dying sparks or even simple empty space.
Below is a sample period-5 negative spaceship, found by Hartmut
Holzwart in March 2007, in a small stabilized section of {zebra
stripes} agar:
.*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*.
.*******************************************************.
.........................................................
.*****************************..***..*******************.
*..............................**...**..................*
.************************..***...**...****..************.
..........................**...............**............
.************************..***...**.....**...**..*******.
*..............................**...*.**........**......*
.************************..***..***...**.....**...******.
..........................**............**.**............
.************************...*****..........**.....******.
*............................*...............**.**......*
.************************.....*.........*.......**..****.
..........................*.*......*...*..........**.....
.************************...*.*.*****......*.......*****.
*..............................***...*......*...........*
.************************...*.*.*****......*.......*****.
..........................*.*......*...*..........**.....
.************************.....*.........*.......**..****.
*............................*...............**.**......*
.************************...*****..........**.....******.
..........................**............**.**............
.************************..***..***...**.....**...******.
*..............................**...*.**........**......*
.************************..***...**.....**...**..*******.
..........................**...............**............
.************************..***...**...****..************.
*..............................**...**..................*
.*****************************..***..*******************.
.........................................................
.*******************************************************.
.*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*.
The "spaceship" travels to the left at {the speed of light}, so it
will eventually reach the edge of any finite patch and destroy itself
and its supporting agar.
:negentropy: (p2) Compare {Hertz oscillator}.
...**.*....
...*.**....
...........
....***....
...*.*.*.**
...**..*.**
**.*...*...
**.*...*...
....***....
...........
....**.*...
....*.**...
:neighbour: Any of the eight cells adjacent to a given cell. A cell is
therefore not considered to be a neighbour of itself, although the
neighbourhood used in Life does in fact include this cell (see
{cellular automaton}).
:new five: (p3) Found by Dean Hickerson, January 1990.
..**.....
.*..*....
.*.*..*..
**.*.**..
*........
.***.****
.....*..*
*.**.....
**.**....
:new gun: An old name for the second known basic {gun} (found, like the
first, by Bill Gosper), shown below. A number of other ways of
constructing a gun from two {twin bees shuttle}s have since been
found - see {edge shooter} for one of these.
.........................**.....**
.........................**.....**
..................................
..................................
..................................
..................................
..................................
..................................
..................................
..................................
..................................
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..................................
...........................**.**..
..........................*.....*.
..................................
.........................*.......*
.........................*..*.*..*
.........................***...***
..................................
..................................
..................................
..................................
.................*................
**...............**...............
**................**..............
.............**..**...............
..................................
..................................
..................................
.............**..**...............
**................**.......**.....
**...............**........**.....
.................*................
:Noah's ark: The following diagonal {puffer} consisting of two {switch
engine}s. This was found by Charles Corderman in 1971. The name
comes from the variety of objects it leaves behind: blocks, blinkers,
beehives, loaves, gliders, ships, boats, long boats, beacons and
block on tables.
..........*.*..
.........*.....
..........*..*.
............***
...............
...............
...............
...............
...............
.*.............
*.*............
...............
*..*...........
..**...........
...*...........
See also {ark}.
:n-omino: Any {polyomino} with exactly n cells.
:nonfiller: = {space nonfiller}
:non-monotonic: A {spaceship} is said to be non-monotonic if its
leading edge falls back in some generations. The first example
(shown below) was found by Hartmut Holzwart in August 1992. This is
p4 and travels at c/4. In April 1994, Holzwart found examples of p3
spaceships with this property, and this is clearly the smallest
possible period. Another non-monotonic spaceship is the {weekender}.
..........**.*.......
......***.*.***......
..*.*..........*...**
**....**.....*...****
..*.**..*....***.*...
........*....*.......
..*.**..*....***.*...
**....**.....*...****
..*.*..........*...**
......***.*.***......
..........**.*.......
:non-spark: Something that looks like a spark, but isn't. An {OWSS}
produces one of these instead of a {belly spark}, and is destroyed by
it.
:non-standard spaceship: Any {spaceship} other than a {glider}, {LWSS},
{MWSS} or {HWSS}.
:non-trivial: A non-trivial period-N oscillator is one in which at
least cell oscillates at the full period. In other words, it is not
made up solely of separate oscillators with smaller periods; it
includes a {spark} or other reaction that would not occur if all
lower-period subpatterns were separated from each other. See
{omniperiodic}.
:NW31: One of the most common stable {edge shooter}s. This
{Herschel-to-glider} {converter} suppresses the junk ordinarily left
behind by an evolving {Herschel} while allowing both the {first
natural glider} and {second natural glider} to escape on {transparent
lane}s:
.......**.......................
........*.......................
........*.*.....................
.........**.....................
................................
................................
................................
..............................**
..............................**
................................
.........*......................
.........*.*....................
.........***....................
...........*....................
................................
................................
................................
................................
..**............................
...*............................
***.............................
*...............................
....................**..........
....................**..........
:NW31T120: The full designator of {NW31}. The T120 timing measurement
means that a canonical NW glider placed at time T=120, at (+31, +0)
relative to the input Herschel, would reach the exact same spacetime
locations as the converter's output glider (assuming no interference
from the conversion circuitry).
:obo spark: A {spark} of the form O.O (so called after its {rle}
encoding).
:octagon II: (p5) The first known p5 {oscillator}, discovered in 1971
independently by Sol Goodman and Arthur Taber. The name is due to
the latter.
...**...
..*..*..
.*....*.
*......*
*......*
.*....*.
..*..*..
...**...
:octagon IV: (p4) Found by Robert Wainwright, January 1979.
.......**.......
.......**.......
................
......****......
.....*....*.....
....*......*....
...*........*...
**.*........*.**
**.*........*.**
...*........*...
....*......*....
.....*....*.....
......****......
................
.......**.......
.......**.......
:octomino: Any 8-cell {polyomino}. There are 369 such objects. The
word is particularly applied to the following octomino (or its
two-generation successor), which is fairly common but lacks a proper
name:
..**
..**
***.
.*..
:odd keys: (p3) Found by Dean Hickerson, August 1989. See also {short
keys} and {bent keys}.
..........*.
.*.......*.*
*.***..**.*.
.*..*..*....
....*..*....
:omino: = {polyomino}
:omniperiodic: A {cellular automaton} is said to be omniperiodic if it
has {oscillator}s of all {period}s. It is not known if Life is
omniperiodic, although this seems likely. Dave Buckingham's work on
Herschel conduits in 1996 (see {My Experience with B-heptominos in
Oscillators}) left only a finite number of unresolved cases, further
reduced by Noam Elkies between 1999 and 2002. At the time of writing
(August 2017) no oscillators are known for periods 19, 23, 38, or 41.
If we insist that the oscillator must contain a cell oscillating at
the full period, then 34 should be added to this list. Period 43 and
53 oscillators were made possible in 2013 by Mike Playle's {Snark}.
Note that if we were to allow infinite oscillators, then all
periods are certainly possible, as any period of 14 or more can be
obtained using a {glider} (or {LWSS}) stream.
:one per generation: See {grow-by-one object}.
:one-sided spaceship synthesis: A {glider synthesis} of a {spaceship}
in which all gliders come from the same side of the spaceship's path.
Such syntheses are used extensively in the 17c/45 {Caterpillar}.
:onion rings: For each integer n>1 onion rings of order n is a {stable}
{agar} of {density} 1/2 obtained by tiling the plane with a certain
4n x 4n pattern. The tile for order 3 onion rings is shown below -
the reader should then be able to deduce the form of tiles of other
orders.
......******
.****.*....*
.*..*.*.**.*
.*..*.*.**.*
.****.*....*
......******
******......
*....*.****.
*.**.*.*..*.
*.**.*.*..*.
*....*.****.
******......
:Online Life-Like CA Soup Search: = {The Online Life-Like CA Soup
Search}.
:on-off: Any p2 {oscillator} in which all {rotor} cells die from
{overpopulation}. The simplest example is a {beacon}. Compare
{flip-flop}.
:O-pentomino: Conway's name for the following {pentomino}, a {traffic
light} {predecessor}, although not one of the more common ones.
*****
:orbit: A term proposed by Jason Summers to refer to a natural
stabilization of a {puffer}. For example, the {switch engine} has
two (known) orbits, the block-laying one and the glider-producing
one.
:Orion: (c/4 diagonally, p4) Found by Hartmut Holzwart, April 1993.
...**.........
...*.*........
...*..........
**.*..........
*....*........
*.**......***.
.....***....**
......***.*.*.
.............*
......*.*.....
.....**.*.....
......*.......
....**.*......
.......*......
.....**.......
In May 1999, Jason Summers found the following smaller variant:
.**..........
**...........
..*..........
....*....***.
....***....**
.....***.*.*.
............*
.....*.*.....
....**.*.....
.....*.......
...**.*......
......*......
....**.......
:orphan: Conway's preferred term for a {Garden of Eden}. According to
some definitions, a orphan consists of just the minimum living and
dead cells needed to ensure that no parent is possible -- whereas a
GoE is an entire infinite Life plane that contains an orphan.
:Orthogonoid: (256c/3476016, p3476016) A {self-constructing} spaceship
with a slow orthogonal direction of travel, analogous to the
{Demonoid}s but using {MWSS}es instead of {glider}s in the
construction recipe. The first example was completed by Dave Greene
on 29 June 2017.
:oscillator: Any pattern that is a {predecessor} of itself. The term
is usually restricted to non-{stable} finite patterns. An oscillator
is divided into a {rotor} and a {stator}. See also {omniperiodic}.
In general {cellular automaton} theory the term "oscillator"
usually covers {spaceship}s as well, but this usage is not normal in
Life.
:Osqrtlogt: (p1 circuitry) A pattern constructed by Adam P. Goucher in
2010, which uses an unbounded triangular region as memory for a
binary counter. Empty space is read as a zero, and a boat is a 1.
The pattern's diametric growth rate is O(sqrt(log(t))), which is the
slowest possible for any Life pattern, or indeed any 2D Euclidean
cellular automaton. Since the population returns infinitely often to
its initial minimum value (during carry operations from 11111...1 to
100000...0, it can be considered to be an unusual form of {sawtooth}.
:OTCA metapixel: (p46 circuitry) A 2048 x 2048 period 35328 {metacell}
constructed by Brice Due in 2006. It contains a large "pixel" area
that contains a large population of {LWSS} spaceships when the cell
state is ON, but is empty when the cell state is OFF. This allows
the state of the cell to be visible at high zoom levels, unlike all
previous unit cells where the state was signaled by the presence or
absence of a single glider in a specific location.
:overclocking: A term used when a {circuit} can accept a signal at a
specific period which it cannot accept at a higher period. A
{syringe} is a simple example. A better example is a {Silver
reflector}, where overclocking creates a situation where the circuit
can process input gliders much faster than the normal {repeat rate}
of 497 ticks, but the stream of gliders has to be continuous. Any
interruption of the stream will cause the destruction of the
reflector.
Some {staged recovery} circuits also permit overclocking, and can
function successfully at a rate faster than their {recovery time}. A
{Silver reflector} has a recovery time of 497 ticks, but can be
overclocked to reflect a period 250 glider stream, or any nearby
period above 248, simply by removing a beehive after the first glider
enters the reflector. However, a continuous stream of gliders is
then required to maintain the circuit, with timing within a tightly
bounded range.
:overcrowding: = {overpopulation}
:over-exposure: = {underpopulation}
:overpopulation: Death of a cell caused by it having more than three
{neighbour}s. See also {underpopulation}.
:overweight spaceship: = {OWSS}
:OWSS: A would-be {spaceship} similar to {LWSS}, {MWSS} and {HWSS} but
longer. On its own an OWSS is unstable, but it can be escorted by
true spaceships to form a {flotilla}.
:Ox: A 1976 novel by Piers Anthony which involves Life.
:p: = {period}
:p15 reflector: A {colour-changing} glider reflector. Compare to the
{colour-preserving} {Snark}. Minimum {repeat time} is 30 ticks.
........................*..
........................*.*
........................**.
...........................
...........................
...........................
...........................
.................*.........
................*..........
................***........
...........................
...**....**.........**.....
..*..*..*..*....**..**.....
..**......**...*.*.........
..**......**....*..........
....**..**.................
..................**.......
..................*........
...................***.....
.*..*.**.*..*........*.....
**..*....*..**.............
.*..*.**.*..*..............
:p1 megacell: (p1 circuitry) A {metacell} constructed by Adam P.
Goucher in 2008, capable of being programmed to emulate any Moore
neighborhood rule, including isotropic and anisotropic non-totalistic
rules. It fits in a 32768 by 32768 bounding box, with the resulting
metacell grid at 45 degrees to the underlying Life grid. Like the
{OTCA metapixel}, it includes a large "pixel" area so that the state
of the megacell can easily be seen even at extremely small-scale zoom
levels.
:p1 telegraph: (p1 circuitry) A variant of Jason Summers' {telegraph}
pattern, constructed in 2010 by Adam P. Goucher using only stable
circuitry. A single incoming glider produces the entire ten-part
composite lightspeed signal that restores the beehive-chain
{lightspeed wire} to its original position. The signal is detected
at the other end of the telegraph and converted back into a single
output signal. This simplification came at the cost of a much slower
transmission speed, one bit per 91080 ticks. In this mechanism,
sending the entire ten-part signal constitutes a '1' bit, and not
sending the signal means '0'.
:p30 shuttle: = {queen bee shuttle}
:p45 glider gun: A {true}-period glider gun discovered by Matthias
Merzenich in April 2010. By most measures this is the smallest known
odd-period gun of any type, either true-period or {pseudo}-period:
.................................................
.................................................
.........................**......................
.....*..*.**.*..*........*.......................
....**..*....*..**.....*.*.......................
.....*..*.**.*..*......**........................
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.................*..*............................
.............**..*..*............................
.............**..*..*.......**...................
............................**....**...*..*...**.
..*...............................*****....*****.
..***.............................**...*..*...**.
.....*......................***..................
....**...........................................
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............................***..................
...........***...................................
...................................*.*...........
....................................**...........
....*......***......................*............
...***...........................................
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............**...................................
...***......**.......*..*..**....................
.....................*..*..**....................
...*.*...............*..*........................
...*.*...........................................
.................................................
...***..........................................*
..............................................*.*
...............................................**
...***...........**......*..*.**.*..*............
....*...........*.*.....**..*....*..**...........
................*........*..*.**.*..*............
...............**................................
.................................................
.................................................
:p46 shuttle: = {twin bees shuttle}
:p4 reflector: The following glider reflector, discovered by Karel
Suhajda in October 2012. Its minimum repeat time is 52 ticks.
Unlike the {pipsquirter}-based reflectors it is a {colour-preserving}
reflector, so it was made obsolete by the discovery of the much
smaller stable {Snark} the following year.
................................*.........................
...............................*..........................
...............................***.......*.*..............
........................................*.**..............
......................................***.....*...........
.....................................*...********.........
..................................*.*.*..*.......*........
..............*...................****.**.*******.*.......
..............***..................***.....*.*..*.*..**...
.................*...................***.*.*...**.*.*.*...
................**.............***..**.*****....*.*.*.....
.............................*.*...***.**.*..*.****..*..**
...........................**.....*....*..*..*...*....*..*
...................*.......**.*.*..*......*..*....*******.
..................*...........*.*..*..*..*.........*......
..................***........*....*..*...........*...**...
............................*.*******........**.*.***.*...
.............................*.........*.*....*.*.*.......
...................**..........*********.***..*.*.........
...................**.......*...*.......*...*.*.*.........
...........................*..*...****..*..*.*.*..........
.............................**...*...*.*.*..*............
.............................*.....***.*.*.**..*..........
........**...............*...***.....*...*...***..........
...**..*..*..................*...**..*..*.**..............
...*....*.*..................*...****...*.*.**............
**.*.....*................***...*......**...*.*...........
.*.*.**....................***.....*..**..*.*.*...........
*..*..*........**...........***..***.***..*.*.**..........
**..*....*.....*.*..........*..*...*...*..*.*.............
.....*****.......*...........*.*..*.**...****.............
................*..........*.*.*.***.***.*................
.......*.........***......*.**.*..**......................
......*.*..........*......*.....*......**.*...............
.......*...................*****......*..**...............
.............................*........**..................
:p54 shuttle: (p54) A surprising variant of the {twin bees shuttle}
found by Dave Buckingham in 1973. See also {centinal}.
**.........................**
.*.........................*.
.*.*.......*.............*.*.
..**.....*..*.....*......**..
............*.....**.........
........*..........**........
........*...**....**.........
.........*****...............
.............................
.........*****...............
........*...**....**.........
........*..........**........
............*.....**.........
..**.....*..*.....*......**..
.*.*.......*.............*.*.
.*.........................*.
**.........................**
:p5 reflector: A {colour-changing} glider reflector constructed by Noam
Elkies in September 1998, by welding together two special-purpose
period-5 {sparker}s. Compare to the {colour-preserving} {Snark}.
Minimum {repeat time} is 25 ticks.
..........................*..
........................**...
.........................**..
.............................
.............................
........**...................
.....*..*.*........*.........
....*.*.*.*.......*..........
...*.*.*..**......***........
...*...*.*..*................
**.**..*.*.*..........**.....
*.*....***..*.....**..**.....
..*.***...**.....*.*.........
..*..*.....*......*..........
...*...*.*..*............**..
....***.**.**.......**....*..
......*....*........**..***..
.......***.*.....**.....***..
..........*.**...**.....**...
.........*..*..***.*........*
.........**..***...........**
................*............
.............****.*..........
............*..*...*.........
............**...*.***.......
.............*.*..*...*......
.............*.**.*..**......
..............*..*...........
...............**............
:p6 pipsquirter: (p6) A {pipsquirter} oscillator found by Noam Elkies
in November 1997, used in various {hassler}s and the colour-changing
{p6 reflector}.
.....*.........
.....*.........
...............
...*...*.......
.***.*.***.....
*...**....*....
*.**..**.*.*...
.*..**..**.*...
..**..**.*.*.**
....*..*.*.*.**
....****.**....
........*......
......*.*......
......**.......
:p6 reflector: (p7) A {colour-changing} glider reflector using the {p6
pipsquirter}. Compare to the {colour-preserving} {Snark}. Minimum
{repeat time} is 24 ticks.
.......................*.
......................*..
......................***
...**....................
...*.....................
.....*...................
....****.........*.......
...*....*.......*........
...*****.*......***......
.**....*.*...............
*..*.....**.........**...
**.*.*.*..*.....**..**...
...*..*.***....*.*.......
...**.*...*.....*........
.....*.*.**..............
.....*.*.*........**.....
......*..*........*......
.......**..........***...
.....................*...
:p6 shuttle: (p6) The following oscillator found by Nicolay Beluchenko
in February 2004.
*.............
***...........
...*..........
..**..........
..............
......*.......
.....****.....
......*..*....
.......***....
..............
..........**..
..........*...
...........***
.............*
This is {extensible} in more than one way:
*........................
***......................
...*.....................
..**.....................
.........................
......*..................
.....****................
......*..*...............
.......***...............
.........................
..........***............
..........*..*...........
...........****..........
.............*...........
.........................
.................*.......
................***......
.................*.*.....
.................*.*.....
..................**.....
.....................**..
.....................*.*.
.......................*.
.......................**
:p72 quasi-shuttle: (p72) The following {oscillator}, found by Jason
Summers in August 2005. Although this looks at first sight like a
{shuttle}, it isn't really.
..............................*......
.............................**......
............................*.**.....
.****......................***..*....
*....*.......................*.*.*...
*...*.*.......................*.*.*..
.*...*.*......**...............*..***
.......*.....*.*................**.*.
.......*.....*...................**..
....*..*.....***.................*...
.....**..............................
.....................................
.....**..............................
....*..*.....***.................*...
.......*.....*...................**..
.......*.....*.*................**.*.
.*...*.*......**...............*..***
*...*.*.......................*.*.*..
*....*.......................*.*.*...
.****......................***..*....
............................*.**.....
.............................**......
..............................*......
:p7 pipsquirter: A {pipsquirter} oscillator found by Noam Elkies in
August 1999, used in various {hassler}s and the colour-changing {p7
reflector}.
................*.....
........*.......*.....
.**...***..*..........
..*..*...***..*...*.**
..*.*.**....***.*.**.*
**..*.*.****....*.....
.*.**........***.****.
.*....*.*.**...*.*..*.
**.*.*.**....*.*......
.*.*......****.*......
.*..******....*.......
**....*..*..*.........
............**........
A larger period-7 pipsquirter is used in cases where space is
limited where the reflector should extend southward for as short a
distance as possible:
.....**..................................
......***................................
....*....*...............................
..******.*.............................*.
.*.....*.**....**.....................*..
.*.**.*....*..*.*.....................***
..*...*.**.*..*..........................
....*.*..*.**.*..........................
...**...*.....**.........................
..*..**.*.****..*...**...................
*..*...*.*...*.*...*.*..........*........
**.*...*..**.*..****..**.......*.........
.*.*.**.*.*.*.*.*...**..*......***.......
*..***..*.....*....*..*.*................
*.*...*.**...**....*.**.**.........**....
.*.****..*..*.*....*.....*.....**..**....
...*...*......**...*..****....*.*........
...*.**..*..*.*....*.....*.....*.........
....*.*.**...**....*.**.**...............
......*.*.....*....*..*.*........**......
......*.*...*.*.*...**..*........*.......
.......*...*.*..****..**..........***....
...........*.*.*...*.*..............*....
............**.**...**...................
:p7 reflector: A {colour-changing} glider reflector using a {p7
pipsquirter}. Compare to the {colour-preserving} {Snark}. Minimum
{repeat time} is 28 ticks. A high-{clearance} version is shown in
{p7 pipsquirter}.
.......................*.
......................*..
......................***
.........................
.........................
.........................
.........................
................*........
......**.......*.........
......*.*......***.......
........*................
...*..*.**.........**....
...****..*.....**..**....
.......***....*.*........
...****..*.....*.........
..*...*.**...............
.*.****.*........**......
.*.*..*.*........*.......
**.*.*.*.**.......***....
*..***.*..*.........*....
..*...*.*................
...**.*.**...............
....*....................
..*.*.****...............
.*.****..*...............
.*.....*.................
..******.*...............
....*...*.*..............
.......*..*..............
........**...............
:p8 G-to-H: A small periodic variant of a stable two-glider-to-Herschel
component found by Paul Callahan in November 1998 and used in the
{Callahan G-to-H}, {Silver reflector} and {Silver G-to-H}. Minimum
{repeat time} is 192 ticks, though some lower periods such as 96 are
possible via {overclocking}. Here a {ghost Herschel} marks the
output signal location:
....*.........*...................
....***.....***...................
.......*...*......................
..*...**...**.....................
...*..............................
.***..............................
..................................
..................................
..................................
...............................*..
...............................*..
....................**.........***
....................**...........*
........**........................
.......*..*.......................
..**....**........................
.*.*..............................
.*................................
**................................
..........**......................
..........*.......................
...........***....................
.............*...........**.......
.....................**..**.......
....................*.*...........
.....................*............
.................*................
................*.*....**.........
...............*...*...*..........
..............*...*.....***.......
.............*...*........*.......
............*...*.................
.............*.*..................
..............*...................
:p8 reflector: A glider {reflector} constructed by Noam Elkies in
September 1998, containing a {figure-8}, boat, eater, and block.
Unlike the {colour-preserving} {Snark}, it is {colour-changing}.
Minimum {repeat time} is 24 ticks.
................*.
...............*..
...............***
..................
..................
..................
..........*.......
.........*........
.........***......
..................
.............**...
.........**..**...
........*.*.......
.........*........
.....*............
....*.*....**.....
...*...*...*......
..*...*.....***...
.*...*........*...
*...*.............
.*.*..............
..*...............
:pair of bookends: = {bookends}
:pair of tables: = {table on table}
:paperclip: (p1)
..**.
.*..*
.*.**
**.*.
*..*.
.**..
:parallel grey ship: = {with-the-grain grey ship}
:Parallel HBK: ((6,3)c/245912, p245912) A much smaller successor to the
{half-baked knightship}, constructed by Chris Cain in September 2014.
Several slow-salvo recipes are needed to support the multi-glider
salvo {seed}s at the upstream end of the spaceship. "Parallel" means
that these recipes are sent in parallel instead of one after the
other, in series, as in the original HBK.
:Parallel HBK gun: an {armless} {constructor} pattern that builds
{Parallel HBK} oblique spaceships every 125906944 ticks, created by
Chris Cain on 3 January 2015.
:parasite: A self-sustaining reaction attached to the output of a rake
or puffer, that damages or modifies the standard output. Compare
{tagalong}. In 2009, while experimenting with novelty generating
patterns in {Golly}, Mitchell Riley discovered parasites on glider
streams from p20 and p8 backward rakes. In some cases, parasites can
even "reproduce", as in the pattern below, though the number of
copies is limited since they will eventually use up their host glider
stream:
......*.............*.........
.....***...........***........
...**.***.........***.**......
....*..*.**.....**.*..*.......
.**.*....*.*...*.*....*.**....
.**.*.*..*.**.**.*..*.*.**....
.*........*.*.*.*........*....
**.......**.*.*.**.......**...
............*.*...............
.......***.*...*.***..........
......**...........**.........
......*.....*....**..*........
.....**....***...**..*........
...........*.**...***.........
............***....*..........
............***...............
............***...............
............**................
..............................
...................*.*........
....................**........
...............**...*.........
........**......**............
.......**......*..............
.........*....................
..............................
..............................
.................**...........
..........*......***..........
.........***.*...***..........
........**.*.....***..........
........**......*.**..........
........**......***....**.....
........**.**....*.....*......
.........**...........**......
..........***.*...*.***.......
...............*.*............
...**.......**.*.*.**.......**
....*........*.*.*.*........*.
....**.*.*..*.**.**.*..*.*.**.
....**.*....*.*...*.*....*.**.
.......*..*.**.....**.*..*....
......**.***.........***.**...
........***...........***.....
.........*.............*......
:parent: A pattern is said to be a parent of the pattern it gives rise
to after one generation. Some patterns have infinitely many parents,
but other have none at all (see {Garden of Eden}).
:parent cells: The three cells that cause a new cell to be born.
:parity: Even or odd, particularly as applied to the {phase} of an
oscillator or spaceship. For example, in {slow salvo} constructions,
the {intermediate target}s are frequently period 2, most often
because they contain {blinker}s or {traffic light}s. A glider
striking a P2 constellation will generally produce a different result
depending on its parity. Period-4 intermediate targets are rare (or
not used), so it doesn't matter if an incoming glider is in phase 1
or phase 3 -- i.e., only the even/odd parity is important.
:PD: = {pentadecathlon}
:pedestle: (p5)
.....*.....
....*.*....
.*..**.....
.***.......
.....***...
...**...*..
..*....*..*
.*.*.*.*.**
.*.*...*.*.
**.*.*.*.*.
*..*....*..
..*...**...
...***.....
.......***.
.....**..*.
....*.*....
.....*.....
:penny lane: (p4) Found by Dave Buckingham, 1972.
...**.....**...
...*.......*...
**.*.......*.**
**.*.*****.*.**
....*..*..*....
.....*****.....
...............
.......*.......
......*.*......
.......*.......
:pentadecathlon: (p15) Found in 1970 by Conway while tracking the
history of short rows of cells, 10 cells giving this object, which is
the most {natural} {oscillator} of period greater than 3. In fact it
is the fifth or sixth most common {oscillator} overall, being about
as frequent as the {clock}, but much less frequent than the
{blinker}, {toad}, {beacon} or {pulsar}.
..*....*..
**.****.**
..*....*..
The pentadecathlon is the only known oscillator which is a
{polyomino} in more than one {phase}.
:pentant: (p5) Found by Dave Buckingham, July 1976.
**........
.*........
.*.*......
..**....**
.........*
.....****.
.....*....
..*...***.
..****..*.
.....*....
....*.....
....**....
:pentaplet: Any 5-cell {polyplet}.
:pentapole: (p2) The {barberpole} of length 5.
**......
*.*.....
........
..*.*...
........
....*.*.
.......*
......**
:pentoad: (p5) Found by Bill Gosper, June 1977. This is {extensible}:
if an eater is moved back four spaces then another {Z-hexomino} can
can be inserted. (This extensibility was discovered by Scott Kim.)
...........**
...........*.
.........*.*.
.........**..
.....**......
......*......
......*......
......**.....
..**.........
.*.*.........
.*...........
**...........
:pentomino: Any 5-cell {polyomino}. There are 12 such patterns, and
Conway assigned them all letters in the range O to Z, loosely based
on their shapes. Only in the case of the {R-pentomino} has Conway's
label remained in common use, but all of them can nonetheless be
found in this lexicon.
:period: The smallest number of generations it takes for an
{oscillator} or {spaceship} to reappear in its original form. The
term can also be used for a {puffer}, {wick}, {fuse}, {superstring},
stream of {spaceship}s, {factory} or {gun}. In the last case there
is a distinction between {true} period and {pseudo} period. There is
also a somewhat different concept of period for {wicktrailer}s.
:period doubler: See {period multiplier}.
:period multiplier: A commonly used term for a {pulse divider}.
Dividing the number of {signal}s in a regular stream by N necessarily
multiplies the {period} by N. For Herschel signals, a number of
small period doubler, tripler, and quadrupler mechanisms are known.
The term "period multiplier" can be somewhat misleading, because most
such circuits can accept input streams that are not strictly
periodic.
:perpendicular grey ship: = {against-the-grain grey ship}
:perturb: To change the fate of an object by reacting it with other
objects. Typically, the other objects are sparks from {spaceship}s
or {oscillator}s, or are {eater}s or impacting spaceships.
Perturbations are typically done to turn a {dirty} reaction into a
{clean} one, or to change the products of a reaction. In many
desirable cases the perturbing objects are not destroyed by the
reaction, or else are easily replenished.
:perturbation: = {perturb}.
:phase: A representative generation of a periodic object such as an
{oscillator} or {spaceship}. The number of phases is equal to the
{period} of the object. The phases of an object usually repeat in
the same cyclic sequence forever, although some {perturbation}s can
cause a {phase change}.
:phase change: A {perturbation} of a periodic object that causes the
object to skip ahead by one or more {phase}s. If the perturbation is
repeated indefinitely, this can effectively change the {period} of
the object. An example of this, found by Dean Hickerson in November
1998, is shown below. In this example, the period of the
{oscillator} would be 7 if the {mold} were removed, but the period is
increased to 8 because of the repeated phase changes caused by the
mold's {spark}.
..........*....
.........*.**..
..**.........*.
..*......*..*.*
.......*...*..*
******.*....**.
*..............
.**.**...**....
..*.*....*.*...
..*.*......*...
...*.......**..
The following pattern demonstrates a p4 c/2 {spaceship} found by
Jason Summers, in which the phase is changed as it deletes a {forward
glider}. This phase change allows the spaceship to be used to delete
a glider wave produced by a {rake} whose period is 2 (mod 4).
........*...........................
.......***.**.......................
......**...*.**.....................
.....**..*.....*....................
......*.....*...*.***...............
.....**.....*...*.*..*..............
...**.*.**....*.*.*...*.............
....*.*..**...........*.............
.**.*..*..*.........*...............
.**.*.....**.........*.***..........
.*.*.............***.*.*.**.........
**.**...........**.*..*.*.*.........
..............**.*...***..**.....**.
.............*...*......*........*.*
............*.....*..**.*.**.....*..
...........*..*.*......*.*..........
...........*.....**....***..........
.............*..........*...........
..........*.*...........*...........
.........**.*.***...................
........*.*.*...*...................
.......**.*.........................
......*...*.....**..................
....................................
......**.**.........................
Phase changing reactions have enabled the construction of
spaceships having periods that were otherwise unknown, and also allow
the construction of period-doubling and period-tripling {convoy}s to
easily produce very high period rakes.
See also {blinker puffer}.
:phi: The following common {spark}. The name comes from the shape in
the generation after the one shown here.
.***.
*...*
*...*
.***.
:phi calculator: (p1 circuitry) See {pi calculator}.
:phoenix: Any pattern all of whose cells die in every generation, but
which never dies as a whole. A {spaceship} cannot be a phoenix, and
in fact every finite phoenix eventually evolves into an {oscillator}.
The following 12-cell oscillator (found by the MIT group in December
1971) is the smallest known phoenix, and is sometimes called simply
"the phoenix".
....*...
..*.*...
......*.
**......
......**
.*......
...*.*..
...*....
Every known phoenix oscillator has period 2. In January 2000,
Stephen Silver showed that a period 3 oscillator cannot be a phoenix.
The situation for higher periods is unknown.
:pi: = {pi-heptomino}
:Pianola breeder: A series of patterns by by Paul Tooke in 2010, based
on a simplification and extension of the {Gemini} spaceship's
construction mechanism. Tooke produced a number of
slow-salvo-constructed patterns with superlinear growth, including a
series of breeder patterns of previously unknown types. For some
patterns, the Gemini's two {construction} arms were moved to a
permanent stationary platform, using fourteen glider-loop channels
instead of twelve.
Some of these breeder patterns remain difficult to classify
unambiguously. For example, one pattern was designed to be an MSS
breeder -- a modified {Gemini} spaceship puffing {slide gun}s which
build lines of {block}s. However, the slide guns produce both moving
and stationary objects at a linear rate, because streams of gliders
are needed to reach out to the construction zone to do the {push}
reaction and build more blocks. The pattern could therefore be
classified as a hybrid MSM/MSS breeder. Other breeder patterns
utilizing slide guns and {universal constructor} technology are
likely to cause similar classification ambiguities.
:pi calculator: (p1 circuitry) A device constructed by Adam P. Goucher
in February 2010, which calculates the decimal digits of pi (the
transcendental number, not the Life pattern!) and displays them in
the Life universe as 8x10 dot matrix characters formed by
arrangements of blocks along a diagonal stripe at the top. A {push}
reaction moves a ten-block diagonal cursor to the next position as
part of the "printing" operation for each new digit.
The actual calculation is done in binary, using a streaming spigot
algorithm based on linear fractional transformations. The pi
calculator is made up of a 188-state computer connected to a printing
device via period-8 {regulator}s and a binary-to-decimal conversion
mechanism. The complete pattern can be found in {Golly}'s Very Large
Patterns online archive, along with the very similar 177-state phi
calculator which uses a simpler algorithm to calculate and print the
Golden Ratio.
:pi climber: The reaction that defines rate of travel of the
{Caterpillar} spaceship. A pi climber consists of a pi-heptomino
"climbing" a chain of blinkers, moving 17 cells every 45 ticks, and
leaving behind an identical chain of blinkers, shifted downward by 6
cells. A single pi climber does not produce any gliders or other
output, but two or more of them traveling on nearby blinker chains
can be arranged to emit gliders every 45 ticks. Compare
{Herschel-pair climber}.
..*..
..*..
..*..
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
.....
..*..
.***.
.*.*.
:pi-heptomino: (stabilizes at time 173) A common pattern. The name is
also applied to later generations of this object - in a {pi ship},
for example, the pi-heptomino itself never arises.
***
*.*
*.*
:pincers: = {great on-off}
:pinwheel: (p4) Found by Simon Norton, April 1970. Compare {clock II}.
......**....
......**....
............
....****....
**.*....*...
**.*..*.*...
...*...**.**
...*.*..*.**
....****....
............
....**......
....**......
:pi orbital: (p168) Found by Noam Elkies, August 1995. In this
{oscillator}, a {pi-heptomino} is turned ninety degrees every 42
generations. A second pi can be inserted to reduce the period to 84.
..............**....**....**...............................
.............*..*.*....*.*..*..............................
.............***..........***..............................
................**......**.................................
...............*..******..*................................
...............**........**................................
...........................................................
........*.............................**..........*........
.......*...***......*.........*.......**.........*.*.......
........*.*****..........***...*...........................
............*...*.....*.*****.*..................*.........
............**....***.....*......................**........
............**....***....**...................*****........
...................*.....**...................**.**.....**.
.................................................*......*.*
.....................................................**.*.*
.....................................................*.*.*.
.......................................................*...
...................................***.........*.*...*..*..
.......**..........................*..*........*..*.....*..
.......**..............................*.......*.*..*...*..
...................................*..*.............*...*..
...................................***..................*..
.....................................................*..*..
................................................*......*...
.............................................**.**...*.*.*.
.............................................*****...**.*.*
.........*......................................**......*.*
........*.*.....................................*.......**.
...........................................................
.**.......*.....................................*.*........
*.*......**......................................*.........
*.*.**...*****.............................................
.*.*.*...**.**.............................................
...*......*................................................
..*..*.....................................................
..*........................................................
..*...*....................................................
..*...*..*.*......................................**.......
..*.....*..*......................................**.......
..*..*...*.*...............................................
...*.......................................................
.*.*.*.....................................................
*.*.**.....................................................
*.*......*.................................................
.**.....**.**...................**.....*...................
........*****...................**....***....**............
........**......................*.....***....**............
.........*..................*.*****.*.....*...*............
...........................*...***..........*****.*........
.......*.*.........**.......*.........*......***...*.......
........*..........**.............................*........
...........................................................
................................**........**...............
................................*..******..*...............
.................................**......**................
..............................***..........***.............
..............................*..*.*....*.*..*.............
...............................**....**....**..............
:pi portraitor: (p32) Found by Robert Wainwright in 1984 or 1985.
Compare with {gourmet} and {popover}.
...........**...........
......**.*....*.**......
......*..........*......
.......**......**.......
....***..******..***....
....*..*........*..*....
.**.*.*..........*.*.**.
.*.*.*............*.*.*.
...*................*...
.*..*..............*..*.
....*.......***....*....
*...*.......*.*....*...*
*...*.......*.*....*...*
....*..............*....
.*..*..............*..*.
...*................*...
.*.*.*............*.*.*.
.**.*.*..........*.*.**.
....*..*........*..*....
....***..******..***....
.......**......**.......
......*..........*......
......**.*....*.**......
...........**...........
:pipsquirt: = {pipsquirter}
:pipsquirter: An {oscillator} that produces a {domino} {spark} that is
orientated parallel to the direction from which it is produced (in
contrast to domino sparkers like the {pentadecathlon} and {HWSS},
which produce domino sparks perpendicular to the direction of
production). See {p6 pipsquirter}, {p7 pipsquirter}.
:pi ship: A {growing spaceship} in which the back part consists of a
{pi-heptomino} travelling at a speed of 3c/10. The first example was
constructed by David Bell. All known pi ships are too large to show
here, but the following diagram shows how the pi fuse works.
............*............
...........*.*...........
**........**.**........**
**.....................**
:piston: (p2) Found in 1971.
**.......**
*.*..*..*.*
..****..*..
*.*..*..*.*
**.......**
:pi wave: A line of {pi-heptomino}es stabilizing one another. For
example, an infinite line of pi-heptominoes arranged as shown below
produces a pi wave that moves at a speed of 3c/10, and leaves no
debris.
***...............***...............***...............***
*.*...............*.*...............*.*...............*.*
*.*...............*.*...............*.*...............*.*
:pixel: = {cell}
:plet: = {polyplet}
:polyomino: A finite collection of orthogonally connected cells. The
mathematical study of polyominoes was initiated by Solomon Golomb in
1953. Conway's early investigations of Life and other cellular
automata involved tracking the histories of small polyominoes, this
being a reasonable way to ascertain the typical behaviour of
different cellular automata when the patterns had to be evolved by
hand rather than by computer. Polyominoes have no special
significance in Life, but their extensive study during the early
years lead to a number of important discoveries and has influenced
the terminology of Life. (Note on spelling: As with "dominoes" the
plural may also be spelt without an e. In this lexicon I have
followed Golomb in using the longer form.)
It is possible for a polyomino to be an {oscillator}. In fact
there are infinitely many examples of such polyominoes, namely the
{cross} and its larger analogues. The only other known examples are
the {block}, the {blinker}, the {toad}, the {star} and (in two
different phases) the {pentadecathlon}.
A polyomino can also be a {spaceship}, as the {LWSS}, {MWSS} and
{HWSS} show.
:polyplet: A finite collection of orthogonally or diagonally connected
cells. This king-wise connectivity is a more natural concept in Life
than the orthogonal connectivity of the {polyomino}.
:pond: (p1)
.**.
*..*
*..*
.**.
:pond on pond: (p1) This term is often used to mean {bi-pond}, but may
also be used of the following {pseudo still life}.
.**...**.
*..*.*..*
*..*.*..*
.**...**.
:popover: (p32) Found by Robert Wainwright in August 1984. Compare
with {gourmet} and {pi portraitor}.
.....................*..........
.....................*..........
.....................***........
.............**.......**........
.............**..***..**........
...................***..........
...................***..........
..............**................
..***........*..*...............
..***........*.*................
***..**...*...*....***..........
.....**...*.....................
....***...*.....................
....*.................**...**...
....*...........***..*..*..**...
........*.......*.*...*.*.......
.......*.*......*.*....*........
...**..*..*................*....
...**...**.................*....
.....................*...***....
.....................*...**.....
..........***........*...**..***
.................**........***..
................*..*.......***..
................*.*.............
..........***....*..............
..........***...................
........**..***..**.............
........**.......**.............
........***.....................
..........*.....................
..........*.....................
:population: The number of ON cells.
:P-pentomino: Conway's name for the following {pentomino}, a common
{spark}.
**
**
*.
:PPS: (c/5 orthogonally, p30) A pre-pulsar spaceship. Any of three
different p30 c/5 orthogonal {spaceship}s in which a {pre-pulsar} is
pushed by a pair of {spider}s. The back sparks of the spaceship can
be used to perturb gliders in many different ways, allowing the easy
construction of c/5 puffers. The first PPS was found by David Bell
in May 1998 based on a p15 pre-pulsar spaceship found by Noam Elkies
in December 1997. See also {SPPS} and {APPS}.
:pre-beehive: The following common {parent} of the {beehive}.
***
***
:pre-block: The following common {parent} of the {block}. Another such
pattern is the {grin}.
*.
**
:precursor: = {predecessor}
:predecessor: Any pattern that evolves into a given pattern after one
or more generations.
:pre-pulsar: A common {predecessor} of the {pulsar}, such as that shown
below. This duplicates itself in 15 generations. (It fails,
however, to be a true {replicator} because of the way the two copies
then interact.)
***...***
*.*...*.*
***...***
A pair of {tub}s can be placed to eat half the pre-pulsar as it
replicates; this gives the p30 oscillator {Eureka} where the
pre-pulsar's replication becomes a movement back and forth. (See
{twirling T-tetsons II} for a variation on this idea.) By other
means the replication of the pre-pulsar can be made to occur in just
14 generations as half of it is eaten; this allows the construction
of p28 and p29 oscillators, and is in fact the only known method for
creating a p29 oscillator. The pre-pulsar is also a vital component
of the only known p47 oscillator.
See also {PPS}.
:pre-pulsar spaceship: = {PPS}.
:pressure cooker: (p3) Found by the MIT group in September 1971.
Compare {mini pressure cooker}.
.....*.....
....*.*....
....*.*....
...**.**...
*.*.....*.*
**.*.*.*.**
...*...*...
...*...*...
....***....
...........
...*.**....
...**.*....
:primer: A pattern originally constructed by Dean Hickerson in November
1991 that emits a stream of {LWSS}s representing the prime numbers.
Some improvements were found by Jason Summers in October 2005.
:PRNG: = {pseudo-random number generator}
:protein: (p3) Found by Dave Buckingham, November 1972.
....**.......
....*........
......*......
..****.*.**..
.*.....*.*..*
.*..**.*.*.**
**.*.....*...
...*..**.*...
...*....*....
....****.....
.............
....**.......
....**.......
:pseudo: Opposite of {true}. A {gun} emitting a period n stream of
spaceships (or rakes) is said to be a pseudo period n gun if its
mechanism oscillates with a period different from n. This period
will necessarily be a multiple of n. Pseudo period n glider guns are
known to exist for all periods greater than or equal to 14, with
smaller periods being impossible. The first pseudo p14 gun was built
by Dieter Leithner in 1995.
The same distinction between true and pseudo also exists for
{puffer}s.
:pseudo-barberpole: (p5) Found by Achim Flammenkamp in August 1994. In
terms of its minimum {population} of 15 this is the smallest known p5
{oscillator}.
..........**
...........*
.........*..
.......*.*..
............
.....*.*....
............
...*.*......
............
..**........
*...........
**..........
:pseudo-random glider generator: A {pseudo-random number generator} in
which the bits are represented by the presence or absence of
{glider}s. The first pseudo-random glider generator was built by
Bill Gosper. David Bell built the first moving one in 1997, using
c/3 {rake}s.
:pseudo-random number generator: A pseudo-random number generator
(PRNG) is an algorithm that produces a sequence of bits that looks
random (but cannot really be random, being algorithmically
determined).
In Life, the term refers to a PRNG implemented as a Life pattern,
with the bits represented by the presence or absence of objects such
as {glider}s or {block}s. Such a PRNG usually contains gliders or
other {spaceship}s in a loop with a feedback mechanism that causes
later spaceships to interfere with the generation of earlier
spaceships. The {period} can be very high, as a loop of n spaceships
has 2^n possible states.
:pseudo still life: The strict definition of {still life} rules out
such stable patterns as the {bi-block}. In such patterns there are
dead cells which have more than 3 neighbours in total, but fewer than
3 in any component still life. These patterns are called pseudo
still lifes. Mark Niemiec has enumerated the pseudo still lifes up
to 24 bits, and his figures are shown below.
-------------
Bits Number
-------------
8 1
9 1
10 7
11 16
12 55
13 110
14 279
15 620
16 1645
17 4067
18 10843
19 27250
20 70637
21 179011
22 462086
23 1184882
24 3068984
-------------
:puffer: An object that moves like a {spaceship}, except that it leaves
debris behind. The first known puffers were found by Bill Gosper and
travelled at c/2 orthogonally (see diagram below for the very first
one, found in 1971). Not long afterwards c/12 diagonal puffers were
found (see {switch engine}). Discounting {wickstretcher}s (which are
not puffers in the conventional sense), no new velocity was obtained
after this until David Bell found the first c/3 orthogonal puffer in
April 1996. Since then c/5 orthogonal puffers have also been found,
the first by Tim Coe in May 1997. Jason Summers built the first c/4
orthogonal puffer in January 1999, and the first 2c/5 orthogonal
puffer in February 1999. Hartmut Holzwart built the first c/4
diagonal puffer (as opposed to a wickstretcher) in February 2004.
.***......*.....*......***.
*..*.....***...***.....*..*
...*....**.*...*.**....*...
...*...................*...
...*..*.............*..*...
...*..**...........**..*...
..*...**...........**...*..
:puffer engine: A pattern which can be used as the main component of a
{puffer}. The pattern may itself be a puffer (e.g. the classic
{puffer train}), it may be a spaceship (e.g. the {Schick engine}), or
it may even be unstable (e.g. the {switch engine}).
:pufferfish: (c/2, p12) A puffer discovered by Richard Schank in
November 2014, from a symmetric soup search using an early version of
{apgsearch}. It consists of a pair of {B-heptomino}es stabilised by
a backend that leaves only pairs of blocks behind. It is simple
enough to be easily synthesized with gliders.
...*.......*...
..***.....***..
.**..*...*..**.
...***...***...
...............
....*.....*....
..*..*...*..*..
*.....*.*.....*
**....*.*....**
......*.*......
...*.*...*.*...
....*.....*....
:pufferfish spaceship: (c/2, p36) Generally, any {spaceship}
constructed using {pufferfish}. May refer specifically to the
extensible c/2 {spaceship} constructed by Ivan Fomichev in December
2014, the first such spaceship to contain no period-2 or period-4
parts. (The first two or three rows might be considered to be period
2 or 4, but they are directly dependent on following rows for
support.).
The pattern consists of two adjacent {pufferfish} spaceships, plus
four copies of a nontrivial period 36 c/2 {fuse} for pufferfish
exhaust, discovered using a randomized soup search.
.......*.......*..................*.......*........
......***.....***................***.....***.......
.....*..**...**..*..............**.*.....*.**......
.....*...*...*...*...............**.*...*.**.......
......**.**.**.**..............*.**.......**.*.....
......**.*...*.**.............*.*..*.*.*.*..*.*....
........*.....*...............*.*...**.**...*.*....
.........**.**.................***.*.....*.***.....
....**..*.....*..**.............***.......***......
....**..*.....*..**.............**.........**......
................................*...........*......
........*.*.*.*................**...........**.....
........**...**................**...........**.....
...................................................
...................................**...**.........
...................*..........*....**...**.........
...*..............***........***..............*....
..***...**...*.*.**.*.......**.*.............***...
.**..*..**.........*........***.............**.*...
.****.*......*...*.*........***.............**.....
**.....*.......**..**.......****..............**...
.*................*..*......*..*...........*..**...
.*.***..*....*.*..**.......**..............*....*..
.*.*...**....*.*..**...*....*.*...........*..*.*...
.**......*..*.......*..*....***..........**...**...
*.....*.*....*.*....*.**................*..........
.**..*..*....*......*.**............*....**........
.**...**.......**...**.**..**......******..........
........................*....*....*.*.*.*.......***
..............................*...*..*.........*...
..............................*....*..........*....
.............................*.................*.*.
:puffer train: The full name for a {puffer}, coined by Conway before
any examples were known. The term was also applied specifically to
the classic puffer train found by Bill Gosper and shown below. This
is very {dirty}, and the tail does not stabilize until generation
5533. It consists of a {B-heptomino} (shown here one generation
before the standard form) escorted by two {LWSS}. (This was the
second known puffer. The first is shown under {puffer}.)
.***...........***
*..*..........*..*
...*....***......*
...*....*..*.....*
..*....*........*.
In April 2006, Jason Summers found a way to make the classic puffer
train into a p20 {spaceship} by adding a {glider} at the back:
***...........***.
*..*..........*..*
*......***....*...
*.....*..*....*...
.*.*..*...*....*.*
.......****.......
.........*........
..................
..................
..................
.......***........
.......*..........
........*.........
:puff suppressor: An attachment at the back of a {line puffer} that
suppresses all or some of its puffing action. The example below (by
Hartmut Holzwart) has a 3-cell puff suppressor at the back which
suppresses the entire puff, making a p2 {spaceship}. If you delete
this puff suppressor then you get a p60 double {beehive} {puffer}.
Puff suppressors were first recognised by Alan Hensel in April 1994.
............*....................
..........**.*...................
..........**...*.................
........*...**.*.....*...........
........****.**...****.......*.*.
......*......*....***.....*.*..*.
......*******...*...*....*..*....
...*.*......**..*...*.*.**....*..
..*********.....*..**........*...
.**..............*.**.****...*..*
**....**.*..........*...*..*.*...
.**....*........***......*.*.*..*
.........*......**......*....**..
.**....*........***......*.*.*..*
**....**.*..........*...*..*.*...
.**..............*.**.****...*..*
..*********.....*..**........*...
...*.*......**..*...*.*.**....*..
......*******...*...*....*..*....
......*......*....***.....*.*..*.
........****.**...****.......*.*.
........*...**.*.....*...........
..........**...*.................
..........**.*...................
............*....................
:pull: A reaction, most often mediated by gliders, that moves an object
closer to the source of the reaction. See {block pull}, {blinker
pull}, {loaf pull}; also {elbow}.
:pulsar: (p3) Despite its size, this is the fourth most common
{oscillator} (and by far the most common of period greater than 2)
and was found very early on by Conway. See also {pre-pulsar} and
{pulsar quadrant}.
..***...***..
.............
*....*.*....*
*....*.*....*
*....*.*....*
..***...***..
.............
..***...***..
*....*.*....*
*....*.*....*
*....*.*....*
.............
..***...***..
:pulsar 18-22-20: = {two pulsar quadrants}
:pulsar CP 48-56-72: = {pulsar} (The numbers refer to the populations
of the three {phase}s.)
:Pulsar Pixel Display: (p30 circuitry) A large-scale raster line
display device constructed by Mark Walsh in August 2010. {Pulsar}s
form the individual pixels in an otherwise empty grid. The published
sample pattern displays and erases eight 7x5-pixel characters on each
of two lines of text.
:pulsar quadrant: (p3) This consists of a quarter of the outer part of
a {pulsar} stabilized by a {cis fuse with two tails}. This is
reminiscent of {mold} and {jam}. Found by Dave Buckingham in July
1973. See also {two pulsar quadrants}.
.....*..
...***..
..*...**
*..*..*.
*...*.*.
*....*..
........
..***...
:pulse: A moving object, such as a {spaceship} or {Herschel}, which can
be used to transmit information. See {pulse divider}.
Also another name for a {pulsar quadrant}.
:pulse divider: A mechanism that lets every n-th object that reaches it
pass through, and deletes all the rest, where n > 1 and the objects
are typically {spaceship}s or {Herschel}s. For n=2, the simplest
known stable pulse divider is the {semi-Snark}.
The following diagram shows a p5 glider pulse divider by Dieter
Leithner (February 1998). The first glider moves the centre block
and is reflected at 90 degrees. The next glider to come along will
not be reflected, but will move the block back to its original
position. The relatively small size and low period of this example
made it useful for constructing compact glider {gun}s of certain
periods, but it became largely obsolete with the discovery of the
semi-Snark. p7, p22, p36 and p46 versions of this pulse divider are
also known.
.....**...................
.....**...................
..........................
..................**......
.................*..*.....
.................*.*..*..*
*...............**.*.*****
.**...........*...**......
**...............**..***..
.............*...*.*..*.*.
........**.......**..**.*.
........**....*...**...*..
................**.*.**...
.................*.*.*....
.................*.*..*...
..................*..**...
..**......................
...*......................
***.......................
*.........................
..........................
............**............
............*.............
.............***..........
...............*..........
:pulshuttle V: (p30) Found by Robert Wainwright, May 1985. Compare
{Eureka}.
.............*..............*.............
............*.*.......*....*.*............
.............*......**.**...*.............
......................*...................
..**......**..................**......**..
*....*..*....*..............*....*..*....*
*....*..*....*..............*....*..*....*
*....*..*....*........*.....*....*..*....*
..**......**........**.**.....**......**..
......................*...................
..........................................
..........................................
..**......**..................**......**..
*....*..*....*........*.....*....*..*....*
*....*..*....*......**.**...*....*..*....*
*....*..*....*........*.....*....*..*....*
..**......**..................**......**..
..........................................
..........................................
......................*...................
..**......**........**.**.....**......**..
*....*..*....*........*.....*....*..*....*
*....*..*....*..............*....*..*....*
*....*..*....*..............*....*..*....*
..**......**..................**......**..
......................*...................
.............*......**.**...*.............
............*.*.......*....*.*............
.............*..............*.............
:pure glider generator: A pattern that evolves into one or more
{glider}s, and nothing else. There was some interest in these early
on, but they are no longer considered important. Here's a neat
example:
..*............
..*............
***............
...............
......***......
.......*.......
............***
............*..
............*..
:push: A reaction that moves an object farther away from the source of
the reaction. See {sliding block memory}, {pi calculator}, {elbow},
{universal constructor}. See also {pull}, {fire}.
:pushalong: Any {tagalong} at the front of a spaceship. The following
is an example (found by David Bell in 1992) attached to the front of
a {MWSS}.
..***.*.....
.****.*.....
**..........
.*.*........
..****.*....
...***......
............
............
......*****.
......*....*
......*.....
.......*...*
.........*..
:pyrotechnecium: (p8) Found by Dave Buckingham in 1972.
.......*........
.....*****......
....*.....*.....
.*..*.*.**.*....
*.*.*.*....*..*.
.*..*....*.*.*.*
....*.**.*.*..*.
.....*.....*....
......*****.....
........*.......
:pyrotechneczum: A common mistaken spelling of {pyrotechnecium}, caused
by a copying error in the early 1990s.
:python: = {long snake}
:Q: = {Quetzal}
:qd: Abbreviation for {quarter diagonal}.
:Q-pentomino: Conway's name for the following {pentomino}, a {traffic
light} {predecessor}.
****
...*
:quad: (p2) Found by Robert Kraus, April 1971. Of all {oscillator}s
that fit in a 6x6 box this is the only {flipper}.
**..**
*..*.*
.*....
....*.
*.*..*
**..**
:QuadLife: A form of {colorized Life} in which there are four types of
ON cell. A newly-born cell takes the type of the majority of its
three {parent cells}, or the remaining type if its parent cells are
all of different types. In areas where there are only two types of
ON cell QuadLife reduces to {Immigration}.
:quadpole: (p2) The {barberpole} of length 4.
**.....
*.*....
.......
..*.*..
.......
....*.*
.....**
:quadratic filter: A toolkit developed by Dean Hickerson and Gabriel
Nivasch in 2006, enabling the construction of patterns with
asymptotic population growth matching an infinite number of different
sublinear functions -- namely, O(t^(1/2^n)) for any chosen n. See
also {exponential filter}, {recursive filter}.
:quadratic growth: The fastest possible asymptotic rate of population
growth for any Life pattern -- O(t^2) in big-O notation, where t is
the number of ticks. The first quadratic-growth pattern found was
Bill Gosper's {breeder}, in 1971; many other types of breeders and
{spacefiller}s have been constructed since.
In April 2011, Stephen Silver gave an example of a one-cell-thick
pattern over a million cells long that exhibited quadratic growth.
In November 2014, Chris Cain constructed a one-cell-thick pattern
with a reduced bounding box of 7242x1.
There are an infinite number of possible growth rates for Life
patterns, between linear and quadratic growth -- see {superlinear
growth}.
:quadratic replicator: A pattern that fills all or part of the Life
plane by making copies of itself in a nonlinear way. Small quadratic
replicators are known in other Life-like rules, but as of January
2016 no example has been found or constructed in Conway's Life.
:quadratic sawtooth: Any {sawtooth} pattern with a quadratic envelope,
or specifically a pattern assembled by Martin Grant in May 2015,
consisting of two caber tossers with period multipliers for timing
which activate and deactivate two toggle rake guns. The gliders
emitted by those rakes annihilate on the diagonal while the rakes are
eaten by 2c/5 ships. All the rakes and gliders are destroyed before
the next cycle. See also {Osqrtlogt}.
:quapole: = {quadpole}
:quarter: (c/4 diagonally, p4) The following {spaceship}, found by
Jason Summers in September 2000. The name is due to the 25-cell
minimum population. This is the smallest known {c/4 spaceship} other
than the {glider}. This spaceship can also be used to make the
smallest known {tubstretcher}.
........**...
.......**....
.........*...
...........**
..........*..
.............
.........*..*
.**.....**...
**.....*.....
..*....*.*...
....**..*....
....**.......
:quarter diagonal: A unit of measurement sometimes used for diagonal
distances, especially for {slow salvo} glider {lane}s. One advantage
of measurement in quarter diagonals is that gliders travel diagonally
at 1qd/tick, so that the same integer value can serve as either a
time or a diagonal distance measurement.
:quasar: (p3) Found by Robert Wainwright, August 1971. See {pulsar}.
..........***...***..........
.............................
........*....*.*....*........
........*....*.*....*........
........*....*.*....*........
..........***...***..........
.............................
........***.......***........
..***..*....*...*....*..***..
.......*....*...*....*.......
*....*.*....*...*....*.*....*
*....*.................*....*
*....*..***.......***..*....*
..***...................***..
.............................
..***...................***..
*....*..***.......***..*....*
*....*.................*....*
*....*.*....*...*....*.*....*
.......*....*...*....*.......
..***..*....*...*....*..***..
........***.......***........
.............................
..........***...***..........
........*....*.*....*........
........*....*.*....*........
........*....*.*....*........
.............................
..........***...***..........
:queen bee: See {queen bee shuttle}.
:queen bee shuttle: (p30) Found by Bill Gosper in 1970. There are a
number of ways to stabilize the ends. Gosper originally stabilized
shuttles against one another in a square of eight shuttles. Two
simpler methods are shown here; for a third see {buckaroo}. The queen
bee shuttle is the basis of all known {true} p30 {gun}s (see {Gosper
glider gun}).
.........*............
.......*.*............
......*.*.............
**...*..*.............
**....*.*.............
.......*.*........**..
.........*........*.*.
....................*.
....................**
:Quetzal: Dieter Leithner's name for the {true} p54 glider gun he built
in January 1998. (This is short for {Quetzalcoatlus} and expresses
the fact that the gun was a very large {Herschel loop} that was not
an {emu}.) Shortly afterwards Leithner also built a p56 Quetzal
using a mechanism found by Noam Elkies for this purpose. In October
1998 Stephen Silver constructed a p55 Quetzal using Elkies' p5
{reflector} of the previous month.
Some of the more recent Quetzals are not Herschel loops, but are
instead short Herschel tracks firing several glider streams all but
one of which is reflected back to the beginning of the track to
create a new Herschel. Noam Elkies first had the idea of doing this
for the p55 case, and Stephen Silver constructed the resulting gun
shortly after building the original (much larger) p55 Quetzal. Jason
Summers later built a p54 version, which is more complicated because
the evenness of the period makes the timing problems considerably
more difficult.
:Quetzalcoatlus: A giant flying dinosaur after which Dieter Leithner
named his p54 gun. Usually abbreviated to {Quetzal}, or simply Q (as
in Q54, Q55, Q56, Q-gun, etc.).
:quilt: = {squaredance}
:R: = {R-pentomino}
:R190: A {composite conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Dave Buckingham in July 1996. It is made up
of two {elementary conduit}s, HRx131B + {BFx59H}. After 190 ticks,
it produces a {Herschel} turned 90 degrees clockwise at (24, 16)
relative to the input. Its {recovery time} is 107 ticks. A {ghost
Herschel} in the pattern below marks the output location:
..........**.........................
.......**..*.........................
.....***.**..........................
....*................................
.*..****.**..........................
.***...*.**..........................
....*................................
...**..........................**....
...............................*.....
.............................*.*.....
.............................**......
.....................................
.....................................
.....................................
.....................................
.................................**.*
.................................*.**
.....................................
*.........................**.........
*.*.......................**.........
***..................................
..*..................................
.....................................
.....................................
.........**...**.....................
..........*...*......................
.......***.....***...................
.......*.........*...................
.................*.*.................
..................**.................
.....................................
.....................................
.....................................
.....................................
.....................................
.........................***.........
.........................*...........
........................**...........
:R2D2: (p8) This was found, in the form shown below, by Peter Raynham
in the early 1970s. The name derives from a form with a larger and
less symmetric {stator} found by Noam Elkies in August 1994. Compare
with {Gray counter}.
.....*.....
....*.*....
...*.*.*...
...*.*.*...
**.*...*.**
**.*...*.**
...*...*...
...*.*.*...
....*.*....
.....*.....
:r5: = {R-pentomino}
:R64: An {elementary conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Dave Buckingham in September 1995. After 64
ticks, it produces a {Herschel} rotated 90 degrees clockwise at (11,
9) relative to the input. Its {recovery time} is 153 ticks, though
this can be improved to 61 ticks by adding a from-the-side eater
inside the turn to avoid interference from the output Herschel's
{first natural glider}, as shown below. A {ghost Herschel} in the
pattern below marks the output location:
..........**...........
..........**.....**....
.................**....
.......................
.......................
...............**......
...............**......
.....................**
.....................**
.......................
.......................
.......................
.*.....................
.*.*...................
.***...................
...*...................
.......................
.......................
.......................
...**.**...............
..*.*.*.*..............
..*.*..*...............
.**.*........***.......
*...**.......*.........
.*.*..*.*...**.........
**.**..**..............
R64 is one of the simplest known {Spartan} conduits, one of the two
known {Blockic} conduits, and one of the few {elementary conduit}s in
the original set of sixteen.
:rabbits: (stabilizes at time 17331) A 9-cell {methuselah} found by
Andrew Trevorrow in 1986.
*...***
***..*.
.*.....
The following {predecessor}, found by Trevorrow in October 1995, has
the same number of cells and lasts two generations longer.
..*....*
**......
.**.***.
:rake: Any {puffer} whose debris consists of {spaceship}s. A rake is
said to be forwards, backwards or sideways according to the direction
of the spaceships relative to the direction of the rake. Originally
the term "rake" was applied only to forwards c/2 glider puffers (see
{space rake}). Many people prefer not to use the term in the case
where the puffed spaceships travel parallel or anti-parallel to the
puffer, as in this case they do not rake out any significant region
of the Life plane (and, in contrast to true rakes, these puffers
cannot travel in a stream, and so could never be produced by a
{gun}).
Although the first rakes (circa 1971) were c/2, rakes of other
velocities have since been built. Dean Hickerson's construction of
{Cordership}s in 1991 made it easy for c/12 diagonal rakes to be
built, although no one actually did this until 1998, by which time
David Bell had constructed c/3 and c/5 rakes (May 1996 and September
1997, respectively). Jason Summers constructed a 2c/5 rake in June
2000 (building on work by Paul Tooke and David Bell) and a c/4
orthogonal rake in October 2000 (based largely on reactions found by
David Bell).
The smallest possible period for a rake is probably 7, as this
could be achieved by a 3c/7 orthogonal backwards glider puffer. The
smallest period attained to date is 8 (Jason Summers, March 2001) -
see {backrake}.
:$rats: (p6) Found by Dave Buckingham, 1972.
.....**.....
......*.....
....*.......
**.*.****...
**.*.....*.*
...*..***.**
...*....*...
....***.*...
.......*....
......*.....
......**....
:R-bee: = {bun}. This name is due to the fact that the pattern is a
single-cell modification of a {beehive}.
:reaction envelope: The collection of {cell}s that are alive during
some part of a given active reaction. This term is used for
{Herschel} {circuit}s and other stable circuitry, whereas
{construction envelope} is specific to recipes in {self-constructing}
circuitry.
There are some subtleties at the edges of the envelope.
Specifically, two reactions that have the exact same set of cells
defining their envelopes may have different behavior when placed next
to a single-cell protrusion like the tail of an {eater1}, or one side
of a {tub}. The difference depends on whether two orthogonally
adjacent cells at the edge of the envelope are ever simultaneously
alive, within the protruding cell's {zone of influence}.
:reburnable fuse: A very rare type of {fuse} whose output is identical
to its input, possibly with some spatial and/or temporal offset.
Reburnable fuses are used primarily in the construction of
fixed-speed {self-supporting} {macro-spaceship}s, where the speed of
the fuse's burning reaction becomes the speed of the spaceship.
Examples include the {Caterpillar}, {Centipede}, and {waterbear}.
:receiver: See {Herschel receiver}.
:recovery time: The number of {ticks} that must elapse after a {signal}
is sent through a {conduit}, before another signal can be safely sent
on the same path. In general, a lower recovery time means a more
useful conduit. For example, the {Snark}'s very low recovery time
allowed for the creation of {oscillator}s with previously unknown
{period}s, 43 and 53.
For the most part this is a synonym for {repeat time}. However,
{overclocking} a complex circuit can often allow it to be used at a
{repeat time} much lower than its safe {recovery time}.
:rectifier: The smallest known 180-degree {reflector}, discovered by
Adam P. Goucher in 2009. It was the smallest and fastest stable
reflector of any kind until the discovery of the {Snark} in 2013. The
rectifier has the same output glider as the {boojum reflector} but a
much shorter {repeat time} of only 106 ticks.
Another advantage of the rectifier is that the output glider is on
a {transparent lane}, so it can be used in logic circuitry to merge
two signal paths.
..*.........................................
*.*.........................................
.**.........................................
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.....**.....................................
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....*.......................................
...**.......................................
..................................**........
.................................*..*..**...
.................................*.*....*...
..............**..................*.....*.**
.............*.*.....................**.*.*.
.............*.......................*..*..*
............**....................*....*..**
..................................*****.....
............................................
....................................**.*....
....................................*.**....
............................***.............
............................*...............
.............................*..............
:recursive filter: A toolkit developed by Alexey Nigin in July 2015,
which enables the construction of patterns with population growth
that asymptotically matches an infinite number of different
superlinear functions. Toolkits enabling other, sublinear infinite
series had been completed by Dean Hickerson and Gabriel Nivasch in
2006 -- see {quadratic filter}, {exponential filter}.
Sublinear functions are possible using the recursive-filter toolkit
as well. It can be used to construct a glider-emitting pattern with
a slowness rate S(X) = O(log***...*(t)), the nth-level iterated
logarithm of t, which asymptotically dominates any
primitive-recursive function f(t).
:reflector: Any {stable} or oscillating pattern that can reflect some
type of {spaceship} (usually a {glider}) without suffering permanent
damage. The first known reflector was the {pentadecathlon}, which
functions as a 180-degree glider reflector (see {relay}). Other
examples include the {buckaroo}, the {twin bees shuttle} and some
oscillators based on the {traffic jam} reaction. Glider {gun}s can
also be made into reflectors, although these are mostly rather large.
In September 1998 Noam Elkies found some fast small-period glider
reflectors. The p8 version is shown below. Replacing the {figure-8}
by the p6 {pipsquirter} gives a p6 version. A more complicated
construction allows a p5 version (which, as had been anticipated,
soon led to a {true} p55 gun - see {Quetzal}). And in August 1999
Elkies found a suitable p7 {sparker}, allowing the first p49
oscillator to be constructed.
......**.....**..
*.*...**.....*...
.**........*.*...
.*.........**....
.......**........
.......*.*.......
........*........
.................
...........***...
...........***...
...........***...
..............***
..............***
..............***
Stable reflectors are special in that if they satisfy certain
conditions they can be used to construct {oscillator}s of all
sufficiently large periods. It was known for some time that stable
reflectors were possible (see {universal constructor}), but no one
was able to construct an explicit example until Paul Callahan did so
in October 1996.
All known stable reflectors are very slow. Callahan's original
reflector has a {repeat time} of 4840, soon improved to 1686 and then
894 and then 850. In November 1996 Dean Hickerson found a variant in
which this is reduced to 747. Dave Buckingham reduced it to 672 in
May 1997 using a somewhat different method, and in October 1997
Stephen Silver reduced it to 623 by a method closer to the original.
In November 1998 Callahan reduced this to 575 with a new initial
reaction. A small modification by Silver a few days later brought
this down to 497.
But in April 2001 Dave Greene found a 180-degree stable reflector
with a repeat time of only 202 (see {boojum reflector}). This
reflector won bounties offered by Dietrich Leithner and Alan Hensel.
Half of the prize money was recycled into a new prize for a small
90-degree reflector, which in turn was won by Mike Playle's
{color-preserving} {Snark} reflector. The Snark is currently the
smallest known stable reflector, with a recovery time of 43. Playle
has offered a $100 prize for a {color-changing} stable reflector
contained within a 25 by 25 {bounding box}, with a recovery time of
50 generations of less.
.
See also {rectifier}, {glider turner}.
:regulator: An object which converts input {glider}s aligned to some
period to output gliders aligned to a different period. The most
interesting case is a {universal regulator}, of which several have
been constructed by Paul Chapman and others. A {stable} universal
regulator was constructed by Dave Greene in September 2015, with a
minimum delay between test signals of 1177 ticks.
:relay: Any {oscillator} in which {spaceship}s (typically {glider}s)
travel in a loop. The simplest example is the p60 one shown below
using two {pentadecathlon}s. Pulling the pentadecathlons further
apart allows any period of the form 60+120n to be achieved - this is
the simplest proof of the existence of oscillators of arbitrarily
large period.
...........................*....*..
................**.......**.****.**
.................**........*....*..
................*..................
..*....*...........................
**.****.**.........................
..*....*...........................
:repeater: Any {oscillator} or {spaceship}.
:repeat time: The minimum number of generations that is possible
between the arrival of one object and the arrival of the next. This
term is used for things such as {reflector}s or {conduit}s where the
{signal} objects ({glider}s or {Herschel}s, for example) will
interact fatally with each other if they are too close together, or
one will interact fatally with a disturbance caused by the other.
For example, the repeat time of Dave Buckingham's 59-step B-heptomino
to Herschel conduit (shown under {conduit}) is 58.
:rephaser: The following reaction that shifts the phase and path of a
pair of gliders. There is another form of this reaction that
reflects the gliders 180 degrees - see {glider-block cycle}.
..*..*..
*.*..*.*
.**..**.
........
........
...**...
...**...
:replicator: A finite pattern which repeatedly creates copies of
itself. Such objects are known to exist (see {universal
constructor}), but no concrete example is known. Dave Greene's
{linear propagator} may be considered to be the first example of a
replicator built in Life, but this is debatable as each of its copies
replicate themselves only once, allowing no possibility of
{superlinear growth}.
:reverse fuse: A {fuse} that produces some initial debris, but then
burns {clean}ly. The following is a simple example.
.............**
............*.*
...........*...
..........*....
.........*.....
........*......
.......*.......
......*........
.....*.........
....*..........
...*...........
..*............
**.............
:revolver: (p2)
*............*
***....*...***
...*.*.*..*...
..*......*.*..
..*.*......*..
...*..*.*.*...
***...*....***
*............*
:ring of fire: (p2) The following {muttering moat} found by Dean
Hickerson in September 1992.
................*.................
..............*.*.*...............
............*.*.*.*.*.............
..........*.*.*.*.*.*.*...........
........*.*.*..**.*.*.*.*.........
......*.*.*.*......*..*.*.*.......
....*.*.*..*..........*.*.*.*.....
.....**.*..............*..*.*.*...
...*...*..................*.**....
....***....................*...*..
..*.........................***...
...**...........................*.
.*...*........................**..
..****.......................*...*
*.............................***.
.***.............................*
*...*.......................****..
..**........................*...*.
.*...........................**...
...***.........................*..
..*...*....................***....
....**.*..................*...*...
...*.*.*..*..............*.**.....
.....*.*.*.*..........*..*.*.*....
.......*.*.*..*......*.*.*.*......
.........*.*.*.*.**..*.*.*........
...........*.*.*.*.*.*.*..........
.............*.*.*.*.*............
...............*.*.*..............
.................*................
:rle: Run-length encoded. Run-length encoding is a simple (but not
very efficient) method of file compression. In Life the term refers
to a specific ASCII encoding used for Life patterns (and patterns for
other similar cellular automata). This encoding was introduced by
Dave Buckingham and is now the usual means of exchanging Life
patterns by email or in online forum discussions.
:R-mango: A small active reaction, so named because it is a single-cell
modification of a {mango}, but now more commonly known as {dove}.
:rock: Dean Hickerson's term for an {eater} which remains intact
throughout the eating process. The {snake} in Dave Buckingham's
59-step B-to-Herschel conduit (shown under {conduit}) is an example.
Other still lifes that sometimes act as rocks include the {tub}, the
{hook with tail}, the {eater1} (eating with its tail) and the {hat}
(in Heinrich Koenig's stabilization of the {twin bees shuttle}).
:roteightor: (p8) Found by Robert Wainwright in 1972.
.*............
.***........**
....*.......*.
...**.....*.*.
..........**..
..............
.....***......
.....*..*.....
.....*........
..**..*...*...
.*.*......*...
.*.......*....
**........***.
............*.
:rotor: The cells of an {oscillator} that change state. Compare
{stator}. It is easy to see that any rotor cell must be adjacent to
another rotor cell.
:R-pentomino: This is by far the most active {polyomino} with less than
six cells: all the others stabilize in at most 10 generations, but
the R-pentomino does not do so until generation 1103, by which time
it has a {population} of 116, including six {glider}s.
.**
**.
.*.
:rule 22: Wolfram's rule 22 is the 2-state 1-D {cellular automaton} in
which a cell is ON in the next generation if and only if exactly one
of its three neighbours is ON in the current generation (a cell being
counted as a neighbour of itself). This is the behaviour of Life on
a cylinder of width 1.
:ruler: A pattern constructed by Dean Hickerson in May 2005 that
produces a stream of {LWSS} with gaps in it, such that the number of
LWSS between successive gaps follows the "ruler function" (sequence
A001511 in The On-Line Encyclopedia of Integer Sequences).
:rumbling river: Any {oscillator} in which the {rotor} is connected and
contained in a strip of width 2. The following p3 example is by Dean
Hickerson, November 1994.
..............**......**......**...*.**..........
....*........*..*....*..*....*..*..**.*..........
*..*.*....*...**..*...**..*...*.*.....*.**.......
****.*..******..******..******..******.*.*.......
.....*.*.....*.*.....*.*.....*.*.....*.*......**.
..**.*.*.*.*...*.*.*...*.*.*...*.*.*...*.*.....*.
.*.....*.*...*.*.*...*.*.*...*.*.*...*.*.*.*.**..
.**......*.*.....*.*.....*.*.....*.*.....*.*.....
.......*.*.******..******..******..******..*.****
.......**.*.....*.*...*..**...*..**...*....*.*..*
..........*.**..*..*....*..*....*..*........*....
..........**.*...**......**......**..............
:Rx202: A {composite conduit}, one of the original sixteen {Herschel
conduit}s, discovered by Dave Buckingham in May 1997. It is made up
of two {elementary conduit}s, HR143B +{BFx59H}.
After 202 ticks, it produces an inverted {Herschel} turned 90 degrees
clockwise at (7, 32) relative to the input. Its {recovery time} is
201 ticks. A {ghost Herschel} in the pattern below marks the output
location:
..............**...............
...........**..*...............
.........***.**......*.........
........*..........***.........
.........***.**...*............
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.........**.........*..*..**...
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.....................*....*..**
.....................*****.....
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.........***...................
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...........**..................
:S: Usually means {big S}, but may sometimes mean {paperclip}.
:sailboat: (p16) A {boat} {hassle}d by a {Kok's galaxy}, a {figure-8}
and two {eater3}s. Found by Robert Wainwright in June 1984.
........*...........*........
.......*.*.........*.*.......
........*...........*........
.............................
......*****.......*****......
.....*....*.......*....*.....
....*..*.............*..*....
.*..*.**.............**.*..*.
*.*.*.....*.......*.....*.*.*
.*..*....*.*.....*.*....*..*.
....**..*..*.....*..*..**....
.........**.......**.........
.............**..............
.............*.*.............
........*..*..*..............
.......*.....................
.....**..........***.........
..*......**.*....***.........
.....*...*..*....***.........
.....***.*...*......***......
..*...........*.....***......
...*...*.***........***......
....*..*...*.................
....*.**......*..............
..........**.................
.........*...................
.....*..*....................
:salvo: A collection of spaceships, usually gliders, all traveling in
the same direction. Any valid glider construction {recipe} can be
partitioned into no more than four salvos. Compare {flotilla}.
:sawtooth: Any finite pattern whose {population} grows without bound
but does not tend to infinity. (In other words, the population
reaches new heights infinitely often, but also infinitely often
returns to some fixed value.) Conway's preferred plural is
"sawteeth".
The first sawtooth was constructed by Dean Hickerson in April 1991.
The current smallest known sawtooth was found by a conwaylife.com
forum user with the online handle 'thunk'. It has a bounding box of
74x60, and is the smallest known sawtooth in terms of its minimum
repeating population of 177 cells. The following variant has a higher
repeating population of 195 and an optimized bounding box of 62x56:
.....................................................**.*.....
.....................................................*.**.....
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Moving sawtooth patterns combining a fast {puffer} with a slower
{spaceship} have also been constructed. See also {tractor beam}.
:SBM: = {sliding block memory}
:Schick engine: (c/2 orthogonally, p12) This {spaceship}, found by Paul
Schick in 1972, produces a large {spark} (the 15 live cells at the
rear in the {phase} shown below) which can be {perturb}ed by other
c/2 spaceships to form a variety of {puffer}s. The diagram below
shows the smallest form of the Schick engine, using two {LWSS}. It
is also possible to use two {MWSS} or two {HWSS}, or even a LWSS and
a HWSS.
****..............
*...*.........*...
*...........**....
.*..*..**.....***.
......***......***
.*..*..**.....***.
*...........**....
*...*.........*...
****..............
:Schick ship: = {Schick engine}
:scorpion: (p1)
...*...
.***...
*...**.
*.*.*.*
.**.*.*
.....*.
:scrubber: (p2) Found in 1971.
....*......
..***......
.*.........
.*..***....
**.*...*...
...*...*...
...*...*.**
....***..*.
.........*.
......***..
......*....
:SE: = {switch engine}
:seal: (c/6 diagonally, p6) The first diagonal {c/6 spaceship}, found
by Nicolay Beluchenko in September 2005.
...*..**..........................
.***.*.*.*........................
.*..***..**.......................
*..******.*.***...................
.*..***.*.*****...................
......*.*.*.*.....................
*.*...*.*.*****...................
*..*.*..*.**...*..................
...*..**.......***................
.*...*****.***..**................
....*.........*...................
..*.*.........*...................
....**.*****...*..................
......*.***..*.....**.............
......*..*...*.***.**.............
........**...***.*..*...*.........
........**....**.****...***.......
...................*.*..*.........
.............*.*.....**..**.......
.............*..*.....*.***.....*.
.............*...*....**..*...*..*
...............***.....**........*
...............*.*..*..*.....**..*
.................*..**.**.*..*....
................*.......*.*.......
.................*...****.........
..................*...*...........
..................................
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.....................**...........
.....................*.*..........
.....................**...........
.......................*..........
......................*...........
:second glider domain: The second glider domain of an {edge shooter} is
the set of displacements (in space and time, relative to the glider
stream emitted by the edge shooter) that a glider stream may have
without interfering with the edge shooter. This is useful to know,
because edge shooters are often used to generate glider streams very
close to other glider streams.
:second natural glider: The glider produced at T=72 during the
evolution of a {Herschel}. This is the common edge-shooting glider
output used in the {NW31} converter and several other converter
variants.
:seed: A {constellation} of still lifes and/or oscillators, which can
be converted into another Life object when it is struck by one or
more gliders. Usually the resulting object is a rare still life or
spaceship, more complex than the original constellation. {Spartan}
single-glider (1G) seeds are more commonly seen than multi-glider
seeds, because a Spartan 1G seed can be readily constructed and
{trigger}ed using a {slow salvo}. See also {freeze-dried salvo}.
For example, the following is a 14{sL} 1G seed for a c/7 loafer
spaceship.
...................................*..........
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...*..........................................
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.*.................*..*.......................
*.*.................**........................
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:Seeds of Destruction Game: An interactive search application written
by Paul Chapman in 2013. Its primary purpose was to assist in the
design of self-destruct circuits in self-constructing circuitry. It
has also regularly been helpful in completing glider syntheses, and
was used to find the {31c/240} base reaction for the {shield bug} and
{Centipede} spaceships.
:self-constructing: A type of pattern, generally a spaceship, that
contains encoded construction information about itself, and makes a
complete copy of itself using those instructions. The {Gemini},
{linear propagator}, {Demonoid}s and {Orthogonoid} are examples of
self-constructing patterns. Self-constructing spaceships often have
trivially adjustable speeds. In many cases, the direction of travel
can also be altered, less easily, by changing the encoded
{construction recipe}. Compare {self-supporting}.
:self-supporting: A type of pattern, specifically a spaceship, that
constructs {signal}s or {track}s or other scaffolding to assist its
movement, but does not contain complete information about its own
structure. Examples include the {Caterpillar}, {Centipede}, {HBK},
{waterbear}, and the {Caterloopillar}s. In general a self-supporting
pattern cannot be trivially adjusted to alter its speed or direction;
the {HBK}'s variable speed is an exception, but its direction of
travel is fixed. Compare {self-constructing}.
:semi-Snark: A small 90-degree {glider reflector} requiring two input
gliders on the same lane for each output glider. It was discovered
by Sergei Petrov on 1 July 2013, using a custom-written search
utility. It functions as a very compact {period doubler} in some
{signal} {circuit}ry, for example the {linear propagator}.
......*..........**
.......**........*.
......**.......*.*.
...............**..
..........*........
**.........**......
**........**.......
...................
...................
.................**
..........**.....**
..........**.......
...................
.....*.............
....*.*............
....**......**.....
............*......
.............***...
...............*...
:sesquihat: (p1) Halfway between a {hat} and a {twinhat}.
....*
**.*.*.
.*.*.*.
.*.*.**
..*...
:SGR: Abbreviation for {stable} {glider} {reflector}. This term is no
longer in use.
:shield bug: (31c/240 orthogonally, p240) The first 31c/240
{macro-spaceship}, constructed by Dave Greene on September 9, 2014.
:shillelagh: (p1)
**...
*..**
.**.*
:ship: (p1) The term is also used as a synonym of {spaceship}.
**.
*.*
.**
:ship in a bottle: (p16) Found by Bill Gosper in August 1994. See also
{bottle}.
....**......**....
...*..*....*..*...
...*.*......*.*...
.**..***..***..**.
*......*..*......*
*.**..........**.*
.*.*..........*.*.
...**...**...**...
.......*.*........
.......**.........
...**........**...
.*.*..........*.*.
*.**..........**.*
*......*..*......*
.**..***..***..**.
...*.*......*.*...
...*..*....*..*...
....**......**....
:ship on boat: = {ship tie boat}
:ship on ship: = {ship-tie}
:ship-tie: (p1) The name is by analogy with {boat-tie}.
**....
*.*...
.**...
...**.
...*.*
....**
:ship tie boat: (p1)
**....
*.*...
.**...
...**.
...*.*
....*.
:short keys: (p3) Found by Dean Hickerson, August 1989. See also {bent
keys} and {odd keys}.
.*........*.
*.***..***.*
.*..*..*..*.
....*..*....
:shoulder: The fixed upper end of a {construction arm}, generally
consisting of one or more glider {gun}s or {edge shooter}s aimed at
an {elbow} object.
:shuttle: Any {oscillator} which consists of an active region moving
back and forth between stabilizing objects. The most well-known
examples are the {queen bee shuttle} (which has often been called
simply "the shuttle") and the {twin bees shuttle}. See also {p54
shuttle} and {Eureka}. Another example is the p72 {R-pentomino}
shuttle that forms part of the pattern given under {factory}.
:siamese: A term used in naming certain {still life}s (and the {stator}
part of certain {oscillator}s). It indicates that the object
consists of two smaller objects sharing two or more cells. See
{snake siamese snake} and {loaf siamese barge} for examples.
:side: Half a {sidewalk}. In itself this is unstable and requires an
{induction coil}.
**...
*.***
....*
:sidecar: A small {tagalong} for a {HWSS} that was found by Hartmut
Holzwart in 1992. The resulting {spaceship} (shown below) has a
{phase} with only 24 cells, making it in this respect the smallest
known spaceship other than the {standard spaceship}s and some trivial
two-spaceship {flotilla}s derived from them. Note also that a HWSS
can support two sidecars at once.
.*......
*.....*.
*.....*.
*****.*.
........
....**..
..*....*
.*......
.*.....*
.******.
:side-shooting gun: = {slide gun}
:sidesnagger: A {Spartan} eater found by Chris Cain in May 2015 with
functionality similar to the eater5, as shown below. It has one
{lane} less diagonal {clearance} on the high-clearance side than
other eater5 variants, due to the presence of the boat. See also
{highway robber}.
.*...........
..*..........
***..........
.............
......*......
.....*.......
.....***.....
.............
.............
......*......
.....*.*.....
....*..*...**
.....**....**
.*...........
*.*..........
**...........
......**.....
......**.....
:side-tracking: See {universal constructor}.
:sidewalk: (p1)
.**.**
..*.*.
.*..*.
.*.*..
**.**.
:siesta: (p5) Found by Dave Buckingham in 1973. Compare {sombreros}.
...........**...
...**.....*.*...
...*.*....*.....
.....*...**.*...
...*.**.....***.
.***.....*.*...*
*...*.*.....***.
.***.....**.*...
...*.**...*.....
.....*....*.*...
...*.*.....**...
...**...........
:signal: Movement of information through the Life universe. Signals
can be carried by {spaceship}s, {fuse}s, {drifter}s, or {conduit}s.
Spaceships can only transfer a signal at the speed of the spaceship,
while fuses can transfer a signal at speeds up to the {speed of
light}.
In practice, many signals are encoded as the presence or absence of
a {glider} or other spaceship at a particular point at a particular
time. Such signals can be combined by the collision of gliders to
form logic operations such as AND, OR, and NOT gates. Signals can be
duplicated using {glider duplicator}s or other {fanout} devices, and
can be used up by causing {perturbation}s on other parts of the Life
object.
Signals are used in {Herschel conduit} circuitry, {universal
constructor}s, {macro-spaceship}s, and other computational patterns
such as the {pi calculator} and {Osqrtlogt} patterns.
:signal elbow: A {conduit} with {signal} output 90 degrees from its
input. This term is commonly used only for signal {wire}s,
particularly {2c/3} signals. A {Snark} could reasonably be called a
"glider elbow", but {glider reflector} is the standard term. A
signal elbow with a {recovery time} less than 20 ticks would enable a
trivial proof that Conway's Life is {omniperiodic}.
Relatively small {composite} {MWSS} elbows can now be constructed,
using Tanner Jacobi's 2015 discovery of a small {H-to-MWSS}
component. The extra beehive can be easily {clean}ed up in various
ways using {Snark}s, {syringe}s or Herschel conduits.
:Silver G-to-H: A variant of the {Silver reflector} made by
substituting an {Fx119} conduit for the final {NW31}, allowing a
Herschel output as well as the beehive-annihilating reset glider. It
is still {Spartan} and retains the {recovery time} of 497 ticks.
:Silver reflector: A {stable} {glider reflector} found by Stephen
Silver in November 1998, by substituting an {NW31} converter for the
second {Fx77} conduit in the {Callahan G-to-H} found a few days
previous. The repeat time is 497 ticks:
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:Silver's p5: (p5) The following oscillator found by Stephen Silver in
February 2000:
**.........
*..........
.*..*......
...**......
...*...*.**
..*....**.*
..**.......
As this has no {spark}, it appears useless. Nonetheless, in March
2000, David Eppstein found a way to use it to reduce the size of Noam
Elkies' p5 {reflector}.
:Simkin glider gun: A {Herschel}-based period 120 glider gun discovered
by Michael Simkin in April 2015. It consists of a Herschel running
through two {B60} conduits. In terms of its 36-cell minimum
population, it is one of the smallest known guns, sharing the record
with the {Gosper glider gun}. In the double-barreled form, as well as
the {pseudo}-period, {snake}-stabilized form shown below, it is the
absolute record holder.
**.....**........................
**.....**........................
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....**...........................
....**...........................
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........................**.*.....
:single-arm: A type of {universal constructor} using just one
construction arm and {slow salvo} techniques to construct, usually,
{Spartan} or near-Spartan circuitry. Compare {two-arm}.
:single-channel: A {universal} construction method discovered by Simon
Ekstrom in December 2015. The initial {elbow operation} toolkit was
near-minimal -- just one {push}, one {pull}, and one output glider of
each colour -- but later searches produced a much larger library.
See {colour of a glider}
:single-lane: = {single-channel}.
:singular flip flop: (p2) Found by Robert Wainwright, July 1972.
..*...
..*.*.
*....*
******
......
..**..
..**..
:sinking ship: = {canoe}
:six Ls: (p3) This is a compact form of {loading dock}.
...*...
.***..*
*...***
***....
....***
***...*
*..***.
...*...
:sixty-nine: (p4) Found by Robert Wainwright, October 1978.
.........*...........
........*.*..........
.....................
......*...**.........
.....*.....*.........
......*.*............
........**......*....
................*....
..*.....**....***....
..*...........**.....
***.......**..**..***
**......*.**....***..
**..***.*.*.....***..
..***................
..***......*.........
..........*.*........
.....................
........*...**.......
.......*.....*.......
........*.*..........
..........**.........
:skewed quad: (p2)
.**....
.*...**
..*.*.*
.......
*.*.*..
**...*.
....**.
:skewed traffic light: (p3) Found by Robert Wainwright, August 1989.
.............**.........
............*..*........
.............*.*........
.........**...*.........
..........*.**..........
............*...........
............*...........
........................
**........***......*....
****.*........*...**....
*.*..***.*....*.........
.........*....*.***..*.*
....**...*........*.****
....*......***........**
........................
...........*............
...........*............
..........**.*..........
.........*...**.........
........*.*.............
........*..*............
.........**.............
:sL: Still life. This abbreviation is used most often in rough
measurements of the complexity of a {Spartan} constellation.
:slide gun: A {gun} which fires sideways from an extending arm. The
arm consists of streams of {spaceship}s which are pushing a pattern
away from the body of the gun and releasing an output spaceship every
time they do so. Each output spaceship therefore travels along a
different path.
Dieter Leithner constructed the first slide gun in July 1994
(although he used the term "side shooting gun"). The following
pattern shows the key reaction of this slide gun. The three gliders
shown will push the block one cell diagonally, thereby extending the
length of the arm by one cell, and at the same time they release an
output glider sideways. (In 1999, Jason Summers constructed slide
guns using other reactions.)
..............**.
..............**.
........***......
..........*......
.........*.....**
..............*.*
................*
.................
.................
.................
.................
.................
.................
.................
.................
.................
.................
.*...............
.**..............
*.*..............
:sliding block memory: A memory register whose value is stored as the
position of a {block}. The block can be moved by means of {glider}
collisions - see {block pusher} for an example.
In Conway's original formulation (as part of his proof of the
existence of a {universal computer} in Life) 2 gliders were used to
pull the block inwards by three diagonal spaces, and 30 gliders were
used to push it out by the same amount. Dean Hickerson later greatly
improved on this, finding a way to pull a block inwards by one
diagonal space using 2 gliders, and push it out using 3 gliders. In
order for the memory to be of any use there also has to be a way to
read the value held. It suffices to be able to check whether the
value is zero (as Conway did), or to be able to detect the transition
from one to zero (as Hickerson did).
Dean Hickerson's sliding block memory is used in Paul Chapman's
{URM}.
:slow elbow: a movable {elbow} in a {construction arm} {toolkit} that
is controlled by a {slow salvo}, which most likely comes from a
previous {construction elbow}. Unlike a standard {elbow} which is
generally fixed on a single {construction lane} or at least within a
narrow range, a slow elbow can move freely in two dimensions as long
as there is room for it.
:slow glider construction: Construction an object by a "slow salvo" of
{glider}s all coming from the same direction, in such a way that
timing of the gliders does not matter as long as they are not too
close behind one another. This type of construction requires an
initial seed object, such as a {block}, which is modified by each
glider in turn until the desired object is produced.
In May 1997, Nick Gotts produced a slow glider construction of a
block-laying switch engine from a block, using a slow salvo of 53
gliders. Constructions like this are important in the study of
{sparse Life}, as they will occur naturally as gliders created in the
first few generations collide with {blonk}s and other debris.
Slow glider constructions are also useful in some designs for
{universal constructor}s. However, in this case the above definition
is usually too restrictive, and it is desirable to allow
constructions in which some gliders in the salvo are required to have
a particular timing modulo 2 (a "p2 slow salvo"). This gives much
greater flexibility, as {blinker}s can now be freely used in the
intermediate construction steps.
:slow salvo: See {slow glider construction}.
:small fish: = {LWSS}
:small lake: (p1) See also {lake}.
....*....
...*.*...
...*.*...
.**...**.
*.......*
.**...**.
...*.*...
...*.*...
....*....
:smiley: (p8) Found by Achim Flammenkamp in July 1994 and named by Alan
Hensel.
**.*.**
...*...
*.....*
.*****.
.......
.......
***.***
:SMM breeder: See {breeder}.
:smoke: Debris which is fairly long-lived but eventually dies
completely. Basically, a large {spark}. This term is used
especially when talking about the output from a {spaceship} - see
{smoking ship}.
:smoking ship: A {spaceship} which produces {smoke}. If the smoke
extends past the edge of the rest of the spaceship, then it can be
used to perturb other objects as the spaceship passes by. Running
gliders into the smoke is often a good way to turn or duplicate the
them, or convert them into other objects. Sometimes the smoke from a
smoking ship may itself be perturbed by accompanying spaceships in
order to form a {puffer}. A simple example of a smoking ship is the
{Schick engine}.
:snacker: (p9) Found by Mark Niemiec in 1972. This is a
{pentadecathlon} with stabilizers which force it into a lower period.
**................**
.*................*.
.*.*............*.*.
..**............**..
.......*....*.......
.....**.****.**.....
.......*....*.......
..**............**..
.*.*............*.*.
.*................*.
**................**
The stabilizers make the {domino} spark largely inaccessible, but the
snacker is {extensible}, as shown in the next diagram, and so a more
accessible p9 domino spark can be obtained. In April 1998 Dean
Hickerson found an alternative stabilizer that is less obtrusive than
the original one, and this is also shown in this diagram.
**................................
.*................................
.*.*.........................**...
..**.......................*..*...
.......*....*..............***....
.....**.****.**...*....*......***.
.......*....*...**.****.**...*...*
..**..............*....*......***.
.*.*.......................***....
.*.........................*..*...
**...........................**... An end can also be stabilized
by killer {candlefrobra}s.
:snail: (c/5 orthogonally, p5) The first known {c/5 spaceship},
discovered by Tim Coe in January 1996. For some time it was the
slowest known orthogonal spaceship.
.*....................................
.*....................................
*.....................................
.***.................***...***........
.**.*.........*...*.*......***........
..*...........**.*.......*....****....
......*......*...*.*...**.*.....**....
...*..*.***...**.........*........**.*
...**.*.....*.....*.................*.
.........*.*******....................
......................................
.........*.*******....................
...**.*.....*.....*.................*.
...*..*.***...**.........*........**.*
......*......*...*.*...**.*.....**....
..*...........**.*.......*....****....
.**.*.........*...*.*......***........
.***.................***...***........
*.....................................
.*....................................
.*....................................
:snake: (p1)
**.*
*.**
:snake bit: An alternative name for a {boat-bit}. Not a very sensible
name, because various other things can be used instead of a snake.
:snake bridge snake: (p1)
....**
....*.
.....*
....**
**.*..
*.**..
:snake dance: (p3) Found by Robert Wainwright, May 1972.
...**.*..
...*.**..
**.*.....
.*..*.***
*..*.*..*
***.*..*.
.....*.**
..**.*...
..*.**...
:snake pit: This term has been used for two different {oscillator}s:
the p2 snake pit (essentially the same as {fore and back})
*.**.**
**.*.*.
......*
***.***
*......
.*.*.**
**.**.*
and the p3 snake pit.
.....**....
....*..*...
....*.**...
.**.*......
*.*.*.****.
*.........*
.****.*.*.*
......*.**.
...**.*....
...*..*....
....**.....
:snake siamese snake: (p1)
**.**.*
*.**.**
:Snark: A small stable 90-degree glider reflector with a repeat time of
43 ticks, discovered by Mike Playle on 25 April 2013 using a search
utility he wrote called {Bellman}. Compare {boojum reflector}. Four
common Snark variants are shown below -- Playle's original (top), and
variants by Heinrich Koenig, Simon Ekstrom, and Shannon Omick (left,
bottom, and right, respectively):
.............................**....................
............................*.*....................
......................**....*......................
....................*..*..**.****..................
....................**.*.*.*.*..*..................
.......................*.*.*.*.....................
.......................*.*.**......................
........................*..........................
...................................................
.....................................**............
............................**.......*.............
............................**.....*.*.............
.........*.........................**..............
.........***.......................................
............*........*.............................
...........**.......*..............................
....................***............................
...................................................
...**..............................................
...*.....................**........................
**.*......................*........................
*..***....**...........***.........................
.**...*...**...........*......................*....
...****.....................**..............*****..
...*...............**........*.............*.....*.
....***............*.*.......*.*............***..*.
.......*.............*........**...............*.**
..*****..............**.....................****..*
.*..*......................*...........**...*...**.
.**......................***...........**....***...
........................*......................*...
........................**.....................*.**
..............................................**.**
...................................................
...................................................
......................................**...........
......................................*............
.......................................***.........
..............**.........................*.........
.............*.*.....**............................
.............*.......**............................
............**.....................................
...................................................
..........................*........................
................**....**.*.*.......................
...............*..*..*.*.*.*.......................
................**...*.*.*.**......................
..................****.**..*.......................
..................*...*....*.......................
...................*..*.***........................
....................*.*.*..........................
.....................*.............................
:SNG: {second natural glider}.
:SODGame: {Seeds of Destruction Game}
:sombrero: One half of {sombreros} or {siesta}.
:sombreros: (p6) Found by Dave Buckingham in 1972. If the two halves
are moved three spaces closer to one another then the period drops to
4, and the result is just a less compact form of {Achim's p4}.
Compare also {siesta}.
...**........**...
...*.*......*.*...
.....*......*.....
...*.**....**.*...
.***..........***.
*...*.*....*.*...*
.***..........***.
...*.**....**.*...
.....*......*.....
...*.*......*.*...
...**........**...
:soup: A random initial pattern, often assumed to cover the whole Life
universe.
:space dust: A part of a {spaceship} or {oscillator} which looks like a
random mix of ON and OFF cells. It is usually very difficult to find
a {glider synthesis} for an object that consists wholly or partly of
space dust.
:spacefiller: Any pattern that grows at a quadratic rate by filling
space with an {agar}. The first example was found in September 1993
by Hartmut Holzwart, following a suggestion by Alan Hensel. The
diagram below shows a smaller spacefiller found by Tim Coe. See also
{Max}. Spacefillers can be considered as {breeder}s (more precisely,
MMS breeders), but they are very different from ordinary breeders.
The word "spacefiller" was suggested by Harold McIntosh and soon
became the accepted term.
..................*........
.................***.......
............***....**......
...........*..***..*.**....
..........*...*.*..*.*.....
..........*....*.*.*.*.**..
............*....*.*...**..
****.....*.*....*...*.***..
*...**.*.***.**.........**.
*.....**.....*.............
.*..**.*..*..*.**..........
.......*.*.*.*.*.*.....****
.*..**.*..*..*..**.*.**...*
*.....**...*.*.*...**.....*
*...**.*.**..*..*..*.**..*.
****.....*.*.*.*.*.*.......
..........**.*..*..*.**..*.
.............*.....**.....*
.**.........**.***.*.**...*
..***.*...*....*.*.....****
..**...*.*....*............
..**.*.*.*.*....*..........
.....*.*..*.*...*..........
....**.*..***..*...........
......**....***............
.......***.................
........*..................
:space nonfiller: Any pattern that expands indefinitely to affect every
cell in the Life plane, but leaves an expanding region of {vacuum} at
its center. Compare {spacefiller}; see also {antstretcher}. The
first nonfiller was discovered by Jason Summers on 14 April 1999:
...................***...............
..................*..*...............
............***......*....***........
............*..*.*...*....*..*.......
............*..*.*...*....*..*.......
..........*..........*..*.*.***......
..........**..**..*.*....*.....*.....
........*................**..***.....
........***.*.**..........*......*...
......*........*.........*.*...***...
......***.....*..........*........*..
...*.*.........................*.***.
..*****.*..........................*.
.**......*.....................*****.
**....**..................*.*........
.*.*...*..*...............*..*...*.*.
........*.*..................**....**
.*****.....................*......**.
.*..........................*.*****..
.***.*.........................*.*...
..*........*..........*.....***......
...***...*.*.........*........*......
...*......*..........**.*.***........
.....***..**................*........
.....*.....*....*.*..**..**..........
......***.*.*..*..........*..........
.......*..*....*...*.*..*............
.......*..*....*...*.*..*............
........***....*......***............
...............*..*..................
...............***...................
:space rake: The following p20 forwards glider {rake}, which was the
first known rake. It consists of an {ecologist} with a {LWSS} added
to turn the dying debris into {glider}s.
...........**.....****
.........**.**...*...*
.........****........*
..........**.....*..*.
......................
........*.............
.......**........**...
......*.........*..*..
.......*****....*..*..
........****...**.**..
...........*....**....
......................
......................
......................
..................****
*..*.............*...*
....*................*
*...*............*..*.
.****.................
:spaceship: Any finite pattern that reappears (without additions or
losses) after a number of generations and displaced by a non-zero
amount. By far the most {natural} spaceships are the {glider},
{LWSS}, {MWSS} and {HWSS}, followed by the {Coe ship} which has also
evolved multiple times from random asymmetric {soup} starting
conditions. See also the entries on individual spaceship speeds:
{c/2 spaceship}, {c/3 spaceship}, {c/4 spaceship}, {c/5 spaceship},
{c/6 spaceship}, {c/7 spaceship}, {c/10 spaceship}, {c/12 spaceship},
{2c/5 spaceship}, {2c/7 spaceship}, {3c/7 spaceship}, and {17c/45
spaceship}.
It is known that there exist spaceships travelling in all rational
directions and at arbitrarily slow speeds (see {universal
constructor}). Before 1989, however, the only known examples
travelled at c/4 diagonally (gliders) or c/2 orthogonally (everything
else).
In 1989 Dean Hickerson started to use automated searches to look
for new {elementary} spaceships, and had considerable success. Other
people have continued these searches using tools such as {lifesrc}
and {gfind}, and as a result we now have a great variety of
elementary spaceships travelling at fifteen different velocities.
The following table details the discovery of elementary spaceships
with new velocities as of August 2017.
----------------------------------------------------------------
Speed Direction First Discovery Discoverer Date
----------------------------------------------------------------
c/4 diagonal {glider} Richard Guy 1970
c/2 orthogonal {LWSS} John Conway 1970
c/3 orthogonal {25P3H1V0.2} Dean Hickerson Aug 1989
c/4 orthogonal {119P4H1V0} Dean Hickerson Dec 1989
c/12 diagonal {Cordership} Dean Hickerson Apr 1991
2c/5 orthogonal {44P5H2V0} Dean Hickerson Jul 1991
c/5 orthogonal {snail} Tim Coe Jan 1996
2c/7 orthogonal {weekender} David Eppstein Jan 2000
c/6 orthogonal {dragon} Paul Tooke Apr 2000
c/5 diagonal {295P5H1V1} Jason Summers Nov 2000
c/6 diagonal {seal} Nicolay Beluchenko Sep 2005
c/7 diagonal {lobster} Matthias Merzenich Aug 2011
c/7 orthogonal {loafer} Josh Ball Feb 2013
c/10 orthogonal {copperhead} zdr Mar 2016
3c/7 orthogonal {spaghetti monster} Tim Coe Jun 2016
----------------------------------------------------------------
Several infinite families of adjustable-velocity {macro-spaceship}s
have also been constructed, of which the first was Gabriel Nivasch's
{Caterpillar} from December 2004. The macro-spaceship with the
widest range of possible speeds is Michael Simkin's {Caterloopillar}
from April 2016; in theory it supports any rational speed strictly
less than c<4. A somewhat similar design supporting any rational
speed strictly less than c/2 has been shown to be feasible, but as of
August 2017 no explicit examples have been constructed.
A period p spaceship that displaces itself (m,n) during its period,
where m>=n, is said to be of type (m,n)/p. It was proved by Conway
in 1970 that p>=2m+2n. (This follows immediately from the
easily-proved fact that a pattern cannot advance diagonally at a rate
greater than one half diagonal step every other generation.)
:Spaceships in Conway's Life: A series of articles posted by David Bell
to the newsgroup comp.theory.cell-automata during the period
August-October 1992 that described many of the new {spaceship}s found
by himself, Dean Hickerson and Hartmut Holzwart. Bell produced an
addendum covering more recent developments in 1996.
:spaghetti monster: The first {3c/7 spaceship}, found by Tim Coe in
June 2016. The spaceship travels orthogonally, has a minimum of 702
live cells and fits in a 27x137 bounding box.
:spark: A pattern that dies. The term is typically used to describe a
collection of cells periodically thrown off by an {oscillator} or
{spaceship}, but other dying patterns, particularly those consisting
or only one or two cells (such as produced by certain glider
collisions, for example), are also described as sparks. For examples
of small sparks see {unix} and {HWSS}. For an example of a much
larger spark see {Schick engine}.
:spark coil: (p2) Found in 1971.
**....**
*.*..*.*
..*..*..
*.*..*.*
**....**
:sparker: An {oscillator} or {spaceship} that produces {spark}s. These
can be used to {perturb} other patterns without being themselves
affected.
:sparky: A certain c/4 {tagalong}, shown here attached to the back of a
{spaceship}.
..........*....................
..........*...............**...
......**.*.***..........**...*.
*.**.**.**..*.*...**.****......
*...**..*.**..***..*.**..**...*
*.**....***.*.***......**..*...
........**.*...............*..*
*.**....***.*.***......**..*...
*...**..*.**..***..*.**..**...*
*.**.**.**..*.*...**.****......
......**.*.***..........**...*.
..........*...............**...
..........*....................
:sparse Life: This refers to the study of the evolution of a Life
universe which starts off as a random {soup} of extremely low
density. Such a universe is dominated at an early stage by {block}s
and {blinker}s (often referred to collectively as {blonk}s) in a
ratio of about 2:1. Much later it will be dominated by simple
{infinite growth} patterns (presumably mostly {switch engine}s). The
long-term fate of a sparse Life universe is less certain. It may
possibly become dominated by self-reproducing patterns (see
{universal constructor}), but it is not at all clear that there is
any mechanism for these to deal with the all junk produced by switch
engines.
:Spartan: A pattern composed of subunits that can be easily constructed
in any orientation, usually with a {slow salvo}. Generally this means
that the pattern is a {constellation} of Spartan still lifes --
{block}, {tub}, {boat}, {hive}, {ship}, {loaf}, {eater1}, or {pond}.
Other small objects may sometimes be counted as Spartan, including
period-2 oscillators -- mainly {blinker}s, but also {beacon}s or
{toad}s, which may occur as {intermediate target}s in slow salvo
{recipe}s. Most {self-constructing} patterns are Spartan or mostly
Spartan, to simplify the process of self-construction.
:speed of light: A speed of one cell per generation, the greatest speed
at which any effect can propagate. Usually denoted c.
:S-pentomino: Conway's name for the following {pentomino}, which
rapidly dies.
..**
***.
:spider: (c/5 orthogonally, p5) This is the smallest known c/5
{spaceship}, and was found by David Bell in April 1997. Its side
{spark}s have proved very useful in constructing c/5 {puffer}s,
including {rake}s. See also {PPS}.
......*...***.....***...*......
...**.*****.**...**.*****.**...
.*.**.*.....*.*.*.*.....*.**.*.
*...*.*...*****.*****...*.*...*
....***.....**...**.....***....
.*..*.***.............***.*..*.
...*.......................*...
:spiral: (p1) Found by Robert Wainwright in 1971.
**....*
.*..***
.*.*...
..*.*..
...*.*.
***..*.
*....**
:spiral growth: A self-constructing pattern built by Dave Greene in
August 2014 that uses four {universal constructor}s (UCs) arranged in
a diamond to build four more UCs in a slightly larger diamond. This
was the first B3/S23 pattern that exhibited spiral growth, and as of
2016 it isthe only such pattern, though a much smaller version could
now be designed with a {single-channel} construction toolkit.
:SPPS: (c/5 orthogonally, p30) The symmetric {PPS}. The original PPS
found by David Bell in May 1998. Compare {APPS}.
:sqrtgun: Any glider-emitting pattern which emits its nth glider at a
time asymptotically proportional to n^2. The first examples were
constructed by Dean Hickerson around 1991. See also {quadratic
filter}, {exponential filter}, {recursive filter}.
:squaredance: The p2 {agar} formed by tiling the plane with the
following pattern. Found by Don Woods in 1971.
**......
....**..
..*....*
..*....*
....**..
**......
...*..*.
...*..*.
:squirter: = {pipsquirter}
:S-spiral: = {big S}
:stable: A pattern is said to be stable if it is a {parent} of itself.
See {still life}.
:staged recovery: A type of signal-processing {circuit} where the
initial reaction between {catalyst}s an incoming signal results in an
imperfect recovery -- a catalyst is damaged, destroyed completely as
in a {bait} reaction, or one or more objects are left behind that
must be cleaned up before the circuit can be reused. In any of these
three cases, output signals from the circuit must be used to complete
the cleanup. In theory the cleanup process might itself be {dirty},
requiring additional cleanup stages. In rare cases this might
theoretically allow the construction of special-purpose circuits with
a lower {recovery time} than would otherwise be possible, but in
practice this kind of situation does not commonly arise.
An example is the record-breaking (at the time) 487-tick reflector
constructed by Adam P. Goucher on 12 April 2009. 487 ticks was a
slight improvement over the repeat time of the {Silver reflector}.
The reflector featured a standard {Callahan G-to-H}, with cleanup by
an internal {dirty} glider reflector found by Dietrich Leithner many
years before -- which in turn was cleaned up by the usual ungainly
Herschel plumbing attached to the G-to-H's output. The dirty glider
reflector is not actually fully recovered before a second p487 signal
enters the full reflector. However, it has been repaired by the time
the internal reflector is actually needed again, so the cycle can be
successfully repeated at p487 instead of p497.
:stairstep hexomino: (stabilizes at time 63) The following
{predecessor} of the {blockade}.
..**
.**.
**..
:stamp collection: A collection of {oscillator}s (or perhaps other Life
objects) in a single diagram, displaying the exhibits much like
stamps in a stamp album. The classic examples are by Dean Hickerson
(see {http://conwaylife.com/ref/DRH/stamps.html}).
:standard spaceship: A {glider}, {LWSS}, {MWSS} or {HWSS}. These have
all been known since 1970.
:star: (p3) Found by Hartmut Holzwart, February 1993.
.....*.....
....***....
..***.***..
..*.....*..
.**.....**.
**.......**
.**.....**.
..*.....*..
..***.***..
....***....
.....*.....
:star gate: A device by Dieter Leithner (October 1996) for transporting
a {LWSS} faster than the {speed of light}. The key reaction is the
{Fast Forward Force Field}.
:stator: The cells of an {oscillator} that are always on. Compare
{rotor}. (The stator is sometimes taken to include also some of
those cells which are always off.) The stator is divided into the
{bushing} and the {casing}.
By analogy, the cells of an {eater} that remain on even when the
eater is eating are considered to constitute the stator of the eater.
This is not always well-defined, because an eater can have more than
one eating action.
:statorless: A statorless {oscillator} is one in which no cell is
permanently on - that is, the {stator} is empty.
:step: Another term for a {generation} or {tick}. This term is
particularly used in describing {conduit}s. For example, a 64-step
conduit is one through which the active object takes 64 generations
to pass.
:stillater: (p3) Found by Robert Wainwright, September 1985. This is
one of only three essentially different p3 {oscillator}s with only
three cells in the {rotor}. The others are {1-2-3} and {cuphook}.
...*....
..*.*.**
..*.**.*
**......
.*.*.**.
.*.*..*.
..*..*..
...**...
:still life: Any {stable} pattern, usually assumed to be finite and
nonempty. For the purposes of enumerating still lifes this
definition is, however, unsatisfactory because, for example, any pair
of blocks would count as a still life, and there would therefore be
an infinite number of 8-bit still lifes. For this reason a stricter
definition is often used, counting a stable pattern as a single still
life only if its {island}s cannot be divided into two nonempty sets
both of which are stable in their own right. Compare {pseudo still
life}.
The requirement that a still life not be decomposable into two
separate stable patterns may seem a bit arbitrary, as it does not
rule out the possibility that it might be decomposable into more than
two. This is shown by the patterns in the following diagram, both
found by Gabriel Nivasch in July 2001. On the left is a 32-cell
pattern that can be broken down into three stable pieces but not into
two. On the right is a 34-cell pattern that can be broken down into
four stable pieces but not into two or three. (Note that, as a
consequence of the Four-Colour Theorem, four is as high as you need
ever go.) It is arguable that patterns like these ought not to be
considered as single still lifes.
......**...........**.
..*.*..*......**.*..*.
.*.**.*.......*.**.*..
.*....**...........**.
**.**.........*.**...*
...**.**....***.**.**.
**....*....*.......*..
.*.**.*.....***.**.*..
*..*.*........*.*.*...
**....................
Still lifes have been enumerated by Conway (4-7 bits), Robert
Wainwright (8-10 bits), Dave Buckingham (11-13 bits), Peter Raynham
(14 bits) and Mark Niemiec (15-24 bits). The resulting figures are
shown below. (These figures shouldn't be affected by the above
discussion of the strict definition of "still life", because it is
unlikely that there are any doubtful cases with much less than 32
cells.)
-------------
Bits Number
-------------
4 2
5 1
6 5
7 4
8 9
9 10
10 25
11 46
12 121
13 240
14 619
15 1353
16 3286
17 7773
18 19044
19 45759
20 112243
21 273188
22 672172
23 1646147
24 4051711
All still lifes up to 18 bits have been shown to be {glider
constructible}. It is an open question whether all still lifes can
be incrementally constructed using glider collisions. For the subset
of small still lifes that have been found to be especially useful in
{self-constructing} circuitry, see also {Spartan}.
:still life tagalong: A {tagalong} which takes the form of a {still
life} in at least one {phase}. An example is shown below.
..**...............
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..****.............
...**..............
...................
...*****...........
..*******..........
.**.*****..........
..**...............
...................
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......*....*...*..*
......**.....*.*..*
.*..*..****.*...**.
*.......**.........
*...*..............
****...............
:stream: A line of identical objects (usually {spaceship}s), each of
which is moving in the same direction, this direction being parallel
to the line. Compare with {wave}.
:stretcher: Any pattern that grows by stretching a {wick} or {agar}.
See {wickstretcher} and {spacefiller}.
:strict volatility: A term suggested by Noam Elkies in August 1998 for
the proportion of cells involved in a period n {oscillator} which
themselves oscillate with period n. For prime n this is the same as
the ordinary {volatility}.
:super beehive: = {honeycomb}
:superfountain: (p4) A p4 {sparker} which produces a 1-cell spark that
is separated from the rest of the oscillator by two clear rows of
cells. The first superfountain was found by Noam Elkies in February
1998. In January 2006 Nicolay Beluchenko found the much smaller one
shown below. See also {fountain}.
...........*...........
.......................
.......................
.....*..*.....*..*.....
...**..*.*****.*..**...
.....*...........*.....
...*.**.........**.*...
.*.*...***...***...*.*.
***.*.............*.***
..........*.*..........
....***...*.*...***....
....*..*...*...*..*....
...****..*.*.*..****...
...**..***.*.***..**...
..*...*...*.*...*...*..
...*..*.*.*.*.*.*..*...
....*.*.**...**.*.*....
.....*...........*.....
:superlinear growth: Growth faster than any rate proportional to T,
where T is the number of ticks that a pattern has been run. This
term usually applies to a pattern's population growth -- e.g.,
{breeder}s' and {spacefiller}s' population asymptotically grows
faster than any linear-growth pattern -- rather than diametric growth
or bounding-box growth. It may also be used to describe the rate of
increase in the number of subpatterns present in a pattern, such as
when describing a {replicator}'s rate of reproduction. Due to limits
enforced by the {speed of light}, no pattern's population can grow at
an asymptotic rate faster than {quadratic growth}.
:superstring: An infinite orthogonal row of cells stabilized on one
side so that it moves at the {speed of light}, often leaving debris
behind. The first examples were found in 1971 by Edward Fitzgerald
and Robert Wainwright. Superstrings were studied extensively by
Peter Rott during 1992-1994, and he found examples with many
different periods. (But no odd periods. In August 1998 Stephen
Silver proved that odd-period superstrings are impossible.)
Sometimes a finite section of a superstring can be made to run
between two tracks ("waveguides"). This gives a {fuse} which can be
made as wide as desired. The first example was found by Tony
Smithurst and uses {tub}s. (This is shown below. The superstring
itself is p4 with a repeating section of width 9 producing one
blinker per period and was one of those discovered in 1971. With the
track in place, however, the period is 8. This track can also be
used with a number of other superstrings.) Shortly after seeing this
example, in March 1997 Peter Rott found another superstring track
consisting of {boat}s. At present these are the only two waveguides
known. Both are destroyed by the superstring as it moves along - it
would be interesting to find one that remains intact.
See {titanic toroidal traveler} for another example of a
superstring.
.**..........................................................
*..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*.
....*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*
*..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*.
.***.........................................................
..**.........................................................
..**.........................................................
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..**.........................................................
..**.........................................................
.***.........................................................
*..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*.
....*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*.*
*..*...*...*...*...*...*...*...*...*...*...*...*...*...*...*.
.**..........................................................
:support: Those parts of an object which are only present in order to
keep the rest of the object (such an {engine} or an edge {spark})
working correctly. These can be components of the object, or else
accompanying objects used to {perturb} the object. In many cases
there is a wide variation of support possible for an engine. The
{arm}s in many {puffer}s are an example of support.
:surprise: (p3) Found by Dave Buckingham, November 1972.
...*....**
...***..*.
.**...*.*.
*..**.*.**
.*......*.
**.*.**..*
.*.*...**.
.*..***...
**....*...
:swan: (c/4 diagonally, p4) A diagonal {spaceship} producing some
useful sparks. Found by Tim Coe in February 1996.
.*..........**..........
*****......**...........
*..**........*.......**.
..**.*.....**......***.*
...........**...*.**....
.....*.*......**........
..........***.*....*....
.......***...*....*.....
........*.......*.......
........*......*........
........................
...........*............
:swimmer: = {switch engine}.
:swimmer lane: = {switch engine channel}.
:switch: A signal-carrying {circuit} that can be modified so that it
cleanly absorbs any future signals instead of allowing them to pass.
Optionally there may be a separate mechanism to restore the circuit
to its original function.
In the following example, a glider from the northeast (shown) will
perform a simple {block pull} that switches off an {F166} conduit, so
that any future Herschel inputs will be cleanly absorbed. A glider
from the southwest (also shown) can restore the block to its original
position.
.**........................................................
..*........................................................
.*.........................................................
.**...............................................**.......
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*...**............................**.......................
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:switchable gun: A {gun} that includes a mechanism to turn the output
stream off and on with simple signals, often gliders. A small
example is Dietrich Leithner's switchable LWSS gun from July 8, 1995.
The ON signal enters from the northeast, and the OFF signal from the
northwest:
.................**...........................................
.................*..*.........................................
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.*.................**.........................................
..*...............*...........................................
***...........................................................
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..................*.*.**....*............*.....**.............
...................****..............*....*....**.............
.....................*...................*....................
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.....................................*.*......................
:switch engine: The following pattern, which in itself is unstable, but
which can be used to make c/12 diagonal {puffer}s and {spaceship}s.
.*.*..
*.....
.*..*.
...***
The switch engine was discovered by Charles Corderman in 1971. He
also found the two basic types of stabilized switch engine: a p288
block-laying type (the more common of the two) and p384
glider-producing type. These two puffers are the most {natural}
infinite growth patterns in Life, being the only ones ever seen to
occur from random starting patterns.
Patterns giving rise to block-laying switch engines can be seen
under {infinite growth}, and one giving rise to a glider-producing
switch engine is shown under {time bomb}. See also {Cordership} and
{ark}.
:switch engine channel: Two lines of {boat}s (or other suitable
objects, such as {tub with tail}s) arranged so that a {switch engine}
can travel between them, in the following manner:
..............**................
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.......***............**........
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David Bell used this in June 2005 to construct a "bobsled"
oscillator, in which a switch engine {factory} sends switch engines
down a channel, at the other end of which they are deleted.
:switch engine chute: = {switch engine channel}
:switch-engine ping-pong: A very large (210515x183739) {quadratic
growth} pattern found by Michael Simkin in October 2014. Currently
this is the smallest starting population (23 cells) known to result
in a quadratic population growth rate.
:synthesis: = {glider synthesis}
:syringe: A small stable glider-to-Herschel converter found by Tanner
Jacobi in March 2015. A second glider can safely follow the first
any time after 78 ticks, but {overclocking} also allows the syringe
to work at a {repeat time} of 74 or 75 ticks. If followed by a
{dependent conduit} a simple {eater2} can be used instead of the
large {weld}ed shown here. A {ghost Herschel} marks the output
location.
....*.............................
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..........................*.*...*.
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.....................**.*..****.*.
.........................*.*...*.*
.....................**.**..*..*.*
......................*.*..**...*.
..........**..........*.*.........
..........**...........*..........
:T: = {T-tetromino}
:table: The following {induction coil}.
****
*..*
:table on table: (p1)
*..*
****
....
****
*..*
:tag: = {tagalong}
:tagalong: An object which is not a {spaceship} in its own right, but
which can be attached to one or more spaceships to form a larger
spaceship. For examples see {Canada goose}, {fly}, {pushalong},
{sidecar} and {sparky}. See also {Schick engine}, which consists of
a tagalong attached to two LWSS (or similar).
The following {c/4 spaceship} (Nicolay Beluchenko, February 2004)
has two wings, either of which can be considered as a tagalong. But
if either wing is removed, then the remaining wing becomes an
essential component of the spaceship, and so is no longer a tagalong.
.......................*.......................
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......**..*.........................*..**......
..**.*.***...........................***.*.**..
.*...*.*...............................*.*...*.
.*...**.................................**...*.
:tail spark: A {spark} at the back of a spaceship. For example, the
1-bit spark at the back of a {LWSS}, {MWSS} or {HWSS} in their less
dense phases.
:tame: To {perturb} a {dirty} reaction using other patterns so as to
make it {clean} and hopefully useful. Or to make a reaction work
which would otherwise fail due to unwanted products which interfere
with the reaction.
:taming: See {tame}.
:tandem glider: Two synchronized gliders traveling at a fixed spacetime
offset, usually as a single signal in a {Herschel transceiver}. See
also {glider pair}.
:target: A necessary component of a {slow salvo} recipe used by a
{single-arm} {universal constructor}. A target usually consists of a
single object, or sometimes a small {constellation} of common still
lifes and/or oscillators. See {intermediate target}. If no {hand}
target is available, a construction arm may be unable to construct
anything, unless recipes are available to generate targets directly
from the {elbow}.
:teardrop: The following {induction coil}, or the formation of two
beehives that it evolves into after 20 generations. (Compare
{butterfly}, where the beehives are five cells further apart.)
***.
*..*
*..*
.**.
:technician: (p5) Found by Dave Buckingham, January 1973.
.....*.....
....*.*....
....**.....
..**.......
.*...***...
*..**...*.*
.**....*.**
...*.*.*...
...*...*...
....***....
......*.*..
.......**..
:technician finished product: = {technician}
:tee: A head-on collision between three gliders, producing a
perpendicular output glider that can be used to construct closely
spaced glider {salvo}s. There are several workable {recipe}s. One
of the more useful is the following, because the {tandem glider} can
be generated by a small {Herschel} {converter}:
...............*.
..............*..
..............***
.........*.......
.........*.*.....
.........**......
.**..............
*.*..............
..*..............
:teeth: A 65-cell quadratic growth pattern found by Nick Gotts in March
2000. This (and a related 65-cell pattern which Gotts found at about
the same time) beat the record previously held by {mosquito5} for
smallest population known to have superlinear growth. Now superseded
by {catacryst}, {metacatacryst}, {Gotts dots} and {wedge}.
:telegraph: A pattern created by Jason Summers in February 2003. It
transmits and receives information using a beehive-chain {lightspeed
wire} -- a rare type of {reburnable fuse} -- at the rate of 1440
ticks per bit. The rate of travel of signals through the entire
{transceiver} device can be increased to any speed strictly less than
the {speed of light} by increasing the length of the chain of
beehives appropriately.
"Telegraph" may also refer to any device that sends and receives
lightspeed signals; see also {p1 telegraph}, {high-bandwidth
telegraph}.
:ternary reaction: Any reaction between three objects. In particular,
a reaction in which two gliders from one stream and one glider from a
crossing stream of the same period annihilate each other. This can
be used to combine two glider guns of the same period to produce a
new glider gun with double the period.
:test tube baby: (p2)
**....**
*.*..*.*
..*..*..
..*..*..
...**...
:tetraplet: Any 4-cell {polyplet}.
:tetromino: Any 4-cell {polyomino}. There are five such objects, shown
below. The first is the {block}, the second is the {T-tetromino} and
the remaining three rapidly evolve into {beehive}s.
**......***......****......***......**.
**.......*...................*.......**
:The Online Life-Like CA Soup Search: A distributed search effort set
up by Nathaniel Johnston in 2009, using a Python script running in
{Golly}. Results included a collection of the longest-lived 20x20
soups, as well as a census of over 174 billion {ash} objects. It has
since been superseded by {Catagolue}.
:The Recursive Universe: A popular science book by William Poundstone
(1985) dealing with the nature of the universe, illuminated by
parallels with the game of Life. This book brought to a wider
audience many of the results that first appeared in {LifeLine}. It
also outlines the proof of the existence of a {universal constructor}
in Life first given in {Winning Ways}.
:thumb: A {spark}-like protrusion which flicks out in a manner
resembling a thumb being flicked. Below on the left is a p9 thumb
sparker found by Dean Hickerson in October 1998. On the right is a
p4 example found by David Eppstein in June 2000.
.......*..............*.....
...**...*.........**...*....
...*.....*.**.....*.....*...
**.*.*......*......***.*.**.
**.*.**.****............**.*
...*.*...........******....*
...*.*.***.......*....*****.
....*.*...*.........*.......
......*..**........*.****...
......**...........*.*..*...
....................*.......
:thunderbird: (stabilizes at time 243)
***
...
.*.
.*.
.*.
:tick: = {generation}
:tie: A term used in naming certain {still life}s (and the {stator}
part of certain {oscillator}s). It indicates that the object
consists of two smaller objects joined point to point, as in {ship
tie boat}.
:time bomb: The following pattern by Doug Petrie, which is really just
a glider-producing {switch engine} in disguise. See {infinite
growth} for some better examples of a similar nature.
.*...........**
*.*....*......*
.......*....*..
..*..*...*..*..
..**......*....
...*...........
:titanic toroidal traveler: The {superstring} with the following
repeating segment. The front part becomes p16, but the eventual fate
of the detached back part is unknown.
******
***...
:TL: = {traffic light}
:T-nosed p4: (p4) Found by Robert Wainwright in October 1989. See also
{filter}.
.....*.....
.....*.....
....***....
...........
...........
...........
...*****...
..*.***.*..
..*.*.*.*..
.**.*.*.**.
*..**.**..*
**.......**
:T-nosed p5: (p5) Found by Nicolay Beluchenko in April 2005.
.....**...............**.**.....*........
..*..*.........**.*.***.**......*........
.*.*.*.....*....*.*.***......**.*........
*..*.*.******.....*....*.*...**.*........
.**.*.*..*...***..*.****..*.*.**.**......
..*.*..**.*..*..*.**....***.*.*....**....
.*..*...*..*.*.**....***...*.............
.*.*.*...***.*...****...*..*.*..**.*..*..
**.*.........**.*....*.*.*.*........*.***
.*.*.*...***.*...****...*..*.*..**.*..*..
.*..*...*..*.*.**....***...*.............
..*.*..**.*..*..*.**....***.*.*....**....
.**.*.*..*...***..*.****..*.*.**.**......
*..*.*.******.....*....*.*...**.*........
.*.*.*.....*....*.*.***......**.*........
..*..*.........**.*.***.**......*........
.....**...............**.**.....*........
:T-nosed p6: (p6) Found by Achim Flammenkamp in September 1994. There
is also a much larger and fully symmetric version found by
Flammenkamp in August 1994.
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..*.*.*.....*.*.*..
***.*.**...**.*.***
..*.*.*.....*.*.*..
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......*.*.*.*......
......**...**......
:toad: (p2) Found by Simon Norton, May 1970. This is the second most
common {oscillator}, although {blinker}s are more than a hundred
times as frequent. See also {killer toads}.
.***
***.
:toad-flipper: A {toad} {hassler} that works in the manner of the
following example. Two {domino} {sparker}s, here {pentadecathlon}s,
apply their {spark}s to the toad in order to flip it over. When the
sparks are applied again it is flipped back. Either or both domino
sparkers can be moved down two spaces from the position shown and the
toad-flipper will still work, but because of symmetry there are
really only two different types. Compare {toad-sucker}.
.*..............*.
.*..............*.
*.*............*.*
.*..............*.
.*......*.......*.
.*......**......*.
.*......**......*.
*.*......*.....*.*
.*..............*.
.*..............*.
:toad-sucker: A {toad} {hassler} that works in the manner of the
following example. Two {domino} {sparker}s, here {pentadecathlon}s,
apply their {spark}s to the toad in order to shift it. When the
sparks are applied again it is shifted back. Either or both domino
sparkers can be moved down two spaces from the position shown and the
toad-sucker will still work, but because of symmetry there are really
only three different types. Compare {toad-flipper}.
.*................
.*..............*.
*.*.............*.
.*.............*.*
.*......*.......*.
.*......**......*.
.*......**......*.
*.*......*......*.
.*.............*.*
.*..............*.
................*.
:toaster: (p5) Found by Dean Hickerson, April 1992.
....*......**..
...*.*.**..*...
...*.*.*.*.*...
..**.*...*.**..
*...**.*.**...*
...*.......*...
...*.......*...
*...**.*.**...*
..**.*...*.**..
...*.*.*.*.*...
...*.*.**..*...
....*......**..
:toggleable gun: Any {gun} that can be turned off or turned on by the
same external signal -- the simplest possible switching mechanism.
An input signal causes the gun to stop producing gliders. Another
input signal from the same source restores the gun to its original
function. Compare {switchable gun}.
Here's a small example by Dean Hickerson from September 1996:
..............**..............*..
..............*.*.............*.*
..............*...............**.
.................................
.................................
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...............*..*....b.........
.****..............*..b..........
*...*..........*...*..bbb........
....*...........****.............
*..*........................aaa..
............................a....
.............................a...
In the figure above, glider B and an LWSS are about to send a glider
NW. Glider A will delete the next glider after B, turning off the
output stream. But if the device were already off, B wouldn't be
present and A would instead delete the leading LWSS, turning the
device back on.
:toggle circuit: Any signal-processing {circuit} that switches back and
forth between two possible states or outputs . An example is the
following alternating H-to-G {converter}:
............*.....................................*........
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..........*****.................................*****......
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*.**......***.........................*.**......***........
.........**..*.................................**..*.......
:TOLLCASS: Acronym for {The Online Life-Like CA Soup Search}.
:toolkit: A set of Life reactions and mechanisms that can be used to
solve any problem in a specific pre-defined class of problems --
{glider} timing adjustment, {salvo} creation, {seed} construction,
etc. See also {universal toolkit}.
:torus: As applies to Life, usually means a finite Life universe which
takes the form of an m x n rectangle with the bottom edge considered
to be joined to the top edge and the left edge joined to the right
edge, so that the universe is topologically a torus. There are also
other less obvious ways of obtaining an toroidal universe.
See also {Klein bottle}.
:total aperiodic: Any finite pattern which evolves in such a way that
no cell in the Life plane is eventually periodic. The first example
was found by Bill Gosper in November 1997. A few days later he found
the following much smaller example consisting of three copies of a
p12 {backrake} by Dave Buckingham.
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:T-pentomino: Conway's name for the following {pentomino}, which is a
common {parent} of the {T-tetromino}.
***
.*.
.*.
:track: A path made out of {conduit}s, often ending where it begins so
that the active {signal} object is cycled forever, forming an
{oscillator} or a {gun}.
This term has also been used to refer to the {lane} on which a
{glider} or {spaceship} travels. The concept is very similar, but a
reference to a "track" now usually implies a non-trivial supporting
conduit.
:tractor beam: A stream of {spaceship}s that can draw an object towards
the source of the stream. The example below shows a tractor beam
pulling a {loaf}; this was used by Dean Hickerson to construct a
{sawtooth}.
.....................*..*......................
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.....*...*..........*...*..........*...*.......
.....*........**....****...........*........**.
.**...*..*...****...........**......*..*...****
*..*........**.**..........**.**..........**.**
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.*...........................**................
:traffic circle: (p100)
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:traffic jam: Any {traffic light} {hassler}, such as {traffic circle}.
The term is also applied to the following reaction, used in most
traffic light hasslers, in which two traffic lights interact in such
a way as to reappear after 25 generations with an extra 6 spaces
between them.
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:traffic light: (p2) A common formation of four blinkers.
..***..
.......
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.......
..***..
:trans-beacon on table: (p2)
....**
.....*
..*...
..**..
......
****..
*..*..
:trans-boat with tail: (p1)
**...
*.*..
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...*.
...**
:transceiver: = {Herschel transceiver}.
:trans-loaf with tail: (p1)
.*....
*.*...
*..*..
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....*.
....**
:transmitter: = {Herschel transmitter}.
:transparent: In signal circuitry, a term used for a {catalyst} that is
completely destroyed by the passing signal, then rebuilt. Often
(though not always) the active reaction passes directly through the
area occupied by the transparent catalyst, then rebuilds the catalyst
behind itself, as in the {transparent block reaction}. See also
{transparent lane}.
:transparent block reaction: A certain reaction between a block and a
{Herschel} {predecessor} in which the block reappears in its original
place some time later, the reaction having effectively passed through
it. This reaction was found by Dave Buckingham in 1988. It has been
used in some {Herschel conduit}s, and in the {gunstar}s. Because the
reaction involves a Herschel predecessor rather than an actual
Herschel, the following diagram shows instead a {B-heptomino} (which
by itself would evolve into a block and a Herschel).
*.............
**..........**
.**.........**
**............
:transparent debris effect: A reaction in which a {Herschel} or other
active region destroys a {still life}, then later, having passed
through the place where the still life was, recreates the still life
in its original position. For an example, see {transparent block
reaction}.
:transparent lane: A path through a signal-producing {circuit} that can
be used to merge signal streams. The signal -- usually a {standard
spaceship} such as a {glider} -- can either be produced by the
circuit, or it can come from elsewhere, passing safely through on the
transparent lane without interacting with the circuit.
:trice tongs: (p3) Found by Robert Wainwright, February 1982. In terms
of its 7x7 {bounding box} this ties with {jam} as the smallest p3
{oscillator}.
..*....
..***..
**...*.
.*.*.*.
.*.....
..**..*
.....**
:trigger: A {signal}, usually a single {glider}, that collides with a
{seed} {constellation} to produce a relatively rare still life or
oscillator, or an output {spaceship} or other signal. The
constellation is destroyed or damaged in the process; compare
{circuit}, {reflector}. Here a pair of trigger gliders strike a
{dirty} seed constellation assembled by Chris Cain in March 2015, to
launch a three-engine {Cordership}:
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:triomino: Either of the two 3-cell {polyomino}es. The term is rarely
used in Life, since the two objects in question are simply the
{blinker} and the {pre-block}.
:triple caterer: (p3) Found by Dean Hickerson, October 1989. Compare
{caterer} and {double caterer}.
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...*...*...*....
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:triplet: Any 3-cell {polyplet}. There are 5 such objects, shown
below. The first two are the two {triomino}es, and the other three
vanish in two generations.
*..................*.......*.......*..
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:tripole: (p2) The {barberpole} of length 3.
**....
*.*...
......
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:tritoad: (p3) Found by Dave Buckingham, October 1977.
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:trivial: A trivial period-N oscillator is one in which every cell
oscillates at some smaller factor of N. See {omniperiodic}.
:true: Opposite of {pseudo}. A {gun} emitting a period n stream of
{spaceship}s (or {rake}s) is said to be a true period n gun if its
mechanism oscillates with period n. (The same distinction between
true and pseudo also exists for {puffer}s.) True period n guns are
known to exist for all periods greater than 61 (see {My Experience
with B-heptominos in Oscillators}), but only a few smaller periods
have been achieved, namely 20, 22, 24, 30, 36, 40, 44, 45, 46, 48,
50, 54, 55, 56, 59 and 60. (Credits for these small period guns are:
p30, p46 and p60 by Bill Gosper in 1970-1971, p44 by Dave Buckingham
in 1992, p50 by Dean Hickerson in 1996, p24 and p48 by Noam Elkies in
1997, p54 and p56 by Dieter Leithner in early 1998, p55 by Stephen
Silver in late 1998, p22 by David Eppstein in 2000, p36 by Jason
Summers in 2004, p59 in 2009 by Adam P. Goucher, p45 in 2010 by
Matthias Merzenich, and p20 and p40 in 2013 also by Merzenich.)
The following diagram shows the p22 gun (David Eppstein, August
2000, using two copies of a p22 oscillator found earlier the same day
by Jason Summers).
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:T-tetromino: The following common {predecessor} of a {traffic light}.
***
.*.
:tub: (p1)
.*.
*.*
.*.
:tubber: (p3) Found by Robert Wainwright before June 1972.
....*.*......
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..*....**....
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:tubeater: A pattern that consumes the output of a {tubstretcher}. The
smallest known tubeater was found by Nicolay Beluchenko (September
2005), and is shown below in conjunction with the smallest known
tubstretcher.
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:tubstretcher: Any {wickstretcher} in which the wick is two diagonal
lines of cells forming, successively, a {tub}, a {barge}, a {long
barge}, etc. The first one was found by Hartmut Holzwart in June
1993, although at the time this was considered to be a boatstretcher
(as it was shown with an extra cell, making the tub into a {boat}).
The following small example is by Nicolay Beluchenko (August 2005),
using a {quarter}.
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:tub with tail: (p1) The following 8-cell {still life}. See {eater}
for a use of this object.
.*...
*.*..
.*.*.
...*.
...**
:tugalong: = {tagalong}
:tumbler: (p14) The smallest known p14 {oscillator}. Found by George
Collins in 1970.
.*.....*.
*.*...*.*
*..*.*..*
..*...*..
..**.**..
:tumbling T-tetson: (p8) A {T-tetromino} {hassle}d by two {figure-8}s.
Found by Robert Wainwright.
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:Turing machine: See {universal computer}.
:turning toads: (p4 wick) Found by Dean Hickerson, October 1989.
..............**.....**.....**.....**.....**..............
.......*.....*......*......*......*......*................
......**...*....*.*....*.*....*.*....*.*....*.*.*.**......
..**.*.***.*..**..*..**..*..**..*..**..*..**..*..*..*.**..
*..*.**.........................................*****.*..*
**.*..............................................**..*.**
...*..................................................*...
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:turtle: (c/3 orthogonally, p3) Found by Dean Hickerson.
.***.......*
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*....*....*.
*....*....*.
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.***.......*
:twin bees shuttle: (p46) Found by Bill Gosper in 1971, this is the
basis of all known p46 oscillators, and so of all known {true} p46
{gun}s (see {new gun} for an example). There are numerous ways to
stabilize the ends, two of which are shown in the diagram. On the
left is David Bell's {double block reaction} (which results in a
shorter, but wider, shuttle than usual), and on the right is the
stabilization by a single block. This latter method produces a very
large {spark} which is useful in a number of ways (see, for example,
{metamorphosis}). Adding a symmetrically placed block below this one
suppresses the spark. See also {p54 shuttle}.
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:twinhat: (p1) See also {hat} and {sesquihat}.
..*...*..
.*.*.*.*.
.*.*.*.*.
**.*.*.**
....*....
:twin peaks: = {twinhat}
:twirling T-tetsons II: (p60) Found by Robert Wainwright. This is a
{pre-pulsar} {hassle}d by {killer toads}.
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:TWIT: = {tub with tail}
:two-arm: The type of {universal constructor} exemplified by the
original {Gemini} spaceship, where two independently programmed
{construction arm}s sent gliders in pairs on 90-degree paths to
collide with each other at the construction site. Construction
recipes for two-arm constructors are much more efficient in general,
but they require many more {circuit}s and multiple independent data
streams, which both tend to increase the complexity of
{self-constructing} circuitry. Compare {single-arm}.
:two eaters: (p3) Found by Bill Gosper, September 1971.
**.......
.*.......
.*.*.....
..**.....
.....**..
.....*.*.
.......*.
.......**
:two pulsar quadrants: (p3) Found by Dave Buckingham, July 1973.
Compare {pulsar quadrant}.
....*....
....*....
...**....
..*......
*..*..***
*...*.*..
*....*...
.........
..***....
:UC: = {universal constructor}.
:underpopulation: Death of a cell caused by it having fewer than two
{neighbour}s. See also {overpopulation}.
:unit cell: See {metacell}.
:unit Life cell: A rectangular pattern, of size greater than 1x1, that
can simulate Life in the following sense. The pattern by itself
represents a dead Life cell, and some other pattern represents a live
Life cell. When the plane is tiled by these two patterns (which then
represent the state of a whole Life universe) they evolve, after a
fixed amount of time, into another tiling of the plane by the same
two patterns which correctly represents the Life generation following
the one they initially represented. It is usual to use capital
letters for the simulated things, so, for example, for the first
known unit Life cell (constructed by David Bell in January 1996), one
Generation is 5760 generations, and one Cell is 500x500 cells.
In December 2005, Jason Summers constructed an analogous unit cell
for Wolfram's Rule 110, a one-dimensional {cellular automaton} that
is known be universal.
:universal: See {universal computer}, {universal constructor},
{universal toolkit}.
:universal computer: A computer that can compute anything that is
computable. (The concept of computability can be defined in terms of
Turing machines, or by Church's lambda calculus, or by a number of
other methods, all of which can be shown to lead to equivalent
definitions.) The relevance of this to Life is that both Bill Gosper
and John Conway proved early on that it is possible to construct a
universal computer in the Life universe. (To prove the universality
of a {cellular automaton} with simple rules was in fact Conway's aim
in Life right from the start.) Conway's proof is outlined in
{Winning Ways}, and also in {The Recursive Universe}.
Until recently, no universal Life computer had ever been built in
practice In April 2000, Paul Rendell completed a Turing machine
construction (see {http://rendell-attic.org/gol/tm.htm} for details).
This, however, has a finite tape, as opposed to the infinite tape of
a true Turing machine, and is therefore not a universal computer.
But in November 2002, Paul Chapman announced the construction of a
universal computer, see
{http://www.igblan.free-online.co.uk/igblan/ca/}. This is a universal
register machine based around Dean Hickerson's {sliding block
memory}.
In 2009 Adam P. Goucher constructed a programmable {Spartan}
universal computer/constructor pattern using stable {Herschel}
circuitry. It included memory tapes and registers capable of holding
a simple universal instruction set and program data, and also a
minimal {single-arm} universal constructor. Its size meant that it
was extremely impractical to program it to be {self-constructing},
though this was theoretically possible -- at least if the escape of
large numbers of gliders could be allowed as a side effect.
In February 2010, Paul Rendell completed a universal Turing machine
design with an unlimited tape, as described in his thesis at
{http://eprints.uwe.ac.uk/22323/1/thesis.pdf}.
In 2016 Nicolas Loizeau ("Coban") completed a Life pattern
emulating a complete 8-bit programmable computer.
See also {universal constructor}.
:universal constructor: A pattern that is capable of constructing
almost any pattern that has a {glider synthesis}. This definition is
a bit vague. A precise definition seems impossible because it has
not been proved that all possible glider fleets are constructible. In
any case, a universal constructor ought to be able to construct
itself in order to qualify as such. An outline of Conway's proof
that such a pattern exists can be found in {Winning Ways}, and also
in {The Recursive Universe}. The key mechanism for the production of
gliders with any given path and timing is known as side-tracking, and
is based on the {kickback reaction}. A universal constructor
designed in this way can also function as a universal destructor - it
can delete almost any pattern that can be deleted by gliders.
In May 2004, Paul Chapman and Dave Greene produced a prototype
programmable universal constructor. This is able to construct
objects by means of {slow glider construction}s. It likely that it
could be programmed to be construct itself, but the necessary program
would be very large; moreover an additional mechanism would be needed
in order to copy the program.
A universal constructor is most useful when attached to a
{universal computer}, which can be programmed to control the
constructor to produce the desired pattern of gliders. In what
follows I will assume that a universal constructor always includes
this computer.
The existence of a universal constructor/destructor has a number of
theoretical consequences.
For example, the constructor could be programmed to make copies of
itself. This is a {replicator}.
The constructor could even be programmed to make just one copy of
itself translated by a certain amount and then delete itself. This
would be a (very large, very high period) {spaceship}. Any
translation is possible (except that it must not be too small), so
that the spaceship could travel in any direction. It could also
travel slower than any given speed, since we could program it to
perform some time-wasting task (such as repeatedly constructing and
deleting a block) before copying itself. Of course, we could also
choose for it to leave some debris behind, thus making a {puffer}.
It is also possible to show that the existence of a universal
constructor implies the existence of a {stable} {reflector}. This
proof is not so easy, however, and is no longer of much significance
now that explicit examples of such reflectors are known.
Progressively smaller universal-constructor mechanisms have been
used in the {linear propagator}, {spiral growth} pattern, and the
{Demonoid}s and {Orthogonoid}.
Another strange consequence of the existence of universal
constructors was pointed out by Adam P. Goucher in 2015. Any
glider-constructible pattern, no matter how large, can be constructed
with a fixed number of gliders, probably less than ten thousand.
This can be done by working out a construction recipe for some type
of {sliding block memory} with a faraway block, attached to a
universal constructor. The block's position encodes an integer value
that can be processed to retrieve as many bits of information as are
needed to build a :1G seed:. Eventually, after a completely
unreasonable number of ticks, the seed can be {trigger}ed to produce
glider salvos which interact to construct the actual target object,
after sending a self-destruct signal to the sliding block memory
unit.
:universal destructor: See {universal constructor}.
:universal register machine: = {URM}
:universal regulator: A {regulator} in which the incoming gliders are
aligned to period 1, that is, they have arbitrary timing (subject to
some minimum time required for the regulator to recover from the
previous glider).
Paul Chapman constructed the first universal regulator in March
2003. It is adjustable, so that the output can be aligned to any
desired period.
:universal toolkit: A set of Life reactions and mechanisms that can be
used to construct any object that can be constructed by glider
collisions.
:unix: (p6) Two {block}s eating a {long barge}. This is a useful
{sparker}, found by Dave Buckingham in February 1976. The name
derives from the fact that it was for some time the mascot of the
Unix lab of the mathematics faculty at the University of Waterloo.
.**.....
.**.....
........
.*......
*.*.....
*..*..**
....*.**
..**....
:up boat with tail: = {trans-boat with tail}
:U-pentomino: Conway's name for the following {pentomino}, which
rapidly dies.
*.*
***
:URM: A universal register machine, particularly Paul Chapman's Life
implementation of such a machine. See {universal computer} for more
information.
:vacuum: Empty space. That is, space containing only dead {cell}s.
:Venetian blinds: The p2 {agar} obtained by using the pattern O..O to
tile the plane. Period 2 stabilizations of finite patches of this
agar are known.
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.....*..*...**.**....*...................*....**.**...*..*.....
....*.*.*......*..**.*.*...............*.*.**..*......*.*.*....
...*..*.**..**..***..**.***************.**..***..**..**.*..*...
...*.**....*.**...**.*********************.**...**.*....**.*...
**.**...**.**....*...........................*....**.**...**.**
*.*...**.*.*..**.*.*.......................*.*.**..*.*.**...*.*
..*.**.*.*..***..**.***********************.**..***..*.*.**.*..
..*.*..****...**.*****************************.**...****..*.*..
.**..*.......*...................................*.......*..**.
*..*.*....**.*.*...............................*.*.**....*.*..*
.*.*..*****..**.*******************************.**..*****..*.*.
..*.***..***.*************************************.***..***.*..
....*.*..*...........................................*..*.*....
..*.*.*..*.*.......................................*.*..*.*.*..
..**...*.**.***************************************.**.*...**..
.........*********************************************.........
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..**...*.**.***************************************.**.*...**..
..*.*.*..*.*.......................................*.*..*.*.*..
....*.*..*...........................................*..*.*....
..*.***..***.*************************************.***..***.*..
.*.*..*****..**.*******************************.**..*****..*.*.
*..*.*....**.*.*...............................*.*.**....*.*..*
.**..*.......*...................................*.......*..**.
..*.*..****...**.*****************************.**...****..*.*..
..*.**.*.*..***..**.***********************.**..***..*.*.**.*..
*.*...**.*.*..**.*.*.......................*.*.**..*.*.**...*.*
**.**...**.**....*...........................*....**.**...**.**
...*.**....*.**...**.*********************.**...**.*....**.*...
...*..*.**..**..***..**.***************.**..***..**..**.*..*...
....*.*.*......*..**.*.*...............*.*.**..*......*.*.*....
.....*..*...**.**....*...................*....**.**...*..*.....
........**..**.*.**...**.*************.**...**.*.**..**........
................**..***..**.*******.**..***..**................
...................*..**.*.*.......*.*.**..*...................
................**.**....*...........*....**.**................
................**.*.**...**.*****.**...**.*.**................
....................**..***..**.**..***..**....................
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.....................*...*..*.*.*.*..*...*.....................
..................**.*.*...**.*.*.**...*.*.**..................
..................*.**.**......*......**.**.*..................
:very long: = {long long}
:very long house: The following {induction coil}.
.*****.
*..*..*
**...**
:volatility: The volatility of an {oscillator} is the size (in cells)
of its {rotor} divided by the sum of the sizes of its rotor and its
{stator}. In other words, it is the proportion of cells involved in
the oscillator which actually oscillate. For many periods there are
known oscillators with volatility 1, see for example {Achim's p16},
{figure-8}, {Kok's galaxy}, {mazing}, {pentadecathlon}, {phoenix},
{relay}, {smiley} and {tumbler}. The smallest period for which the
existence of such statorless oscillators is undecided is 3, although
Dean Hickerson showed in 1994 that there are p3 oscillators with
volatility arbitrarily close to 1 (as is the case for all but
finitely many periods, because of the possibility of feeding the
gliders from a {true} period n {gun} into an {eater}).
The term "volatility" is due to Robert Wainwright. See also
{strict volatility}.
:volcano: Any of a number of p5 oscillators which produce sparks. See
{lightweight volcano}, {middleweight volcano} and {heavyweight
volcano}.
:von Neumann neighbourhood: The set of all cells that are orthogonally
adjacent to a cell or group of cells. The von Neumann neighbourhood
of a cell can be thought of as the points at a Manhattan distance of
1 from that cell. Compare {Moore neighbourhood}.
Cell neighbourhoods can also be defined with a higher range. The
von Neumann neighbourhood of range n can be defined recursively as
the von Neumann neighbourhood of the von Neumann neighbourhood of
range n-1. For example, the von Neumann neighbourhood of range 2 is
the set of all cells that are orthogonally adjacent to the range-1
von Neumann neighbourhood.
:V-pentomino: Conway's name for the following {pentomino}, a {loaf}
{predecessor}.
*..
*..
***
:Wainwright's tagalong: A small p4 c/4 diagonal {tagalong} that has 7
cells in every phase. It is shown here attached to the back of a
{Canada goose}.
***.............
*.........**....
.*......***.*...
...**..**.......
....*...........
........*.....*.
....**...*...**.
...*.*.**....*.*
...*.*..*.**.*..
..*....**.....*.
..**............
..**............
:washerwoman: (2c/3 p18 fuse) A {fuse} by Earl Abbe.
*.......................................................
**....*.....*.....*.....*.....*.....*.....*.....*.....*.
***..*.*...*.*...*.*...*.*...*.*...*.*...*.*...*.*...*.*
**....*.....*.....*.....*.....*.....*.....*.....*.....*.
*.......................................................
:washing machine: (p2) Found by Robert Wainwright before June 1972.
.**.**.
*.**..*
**....*
.*...*.
*....**
*..**.*
.**.**.
:wasp: (c/3 orthogonally, p3) The following {spaceship} which produces
a {domino} {spark} at the back. It is useful for {perturb}ing other
objects. Found by David Bell, March 1998.
..........**.**.......
........**.*.**.**....
.....***.*..***..****.
.***....***.....*....*
*.*.*.***.*........**.
*.*.*.****............
.*.*....*..*..........
..........*...........
..*...................
..*...................
:waterbear: ((23,5)c/79 obliquely, p158) A {self-supporting} oblique
{macro-spaceship} constructed by Brett Berger on December 28, 2014.
It is currently the fastest oblique spaceship in Conway's Game of
Life by several orders of magnitude, and is also the smallest known
oblique spaceship in terms of bounding box, superseding the {Parallel
HBK}. Previous oblique spaceships, the {Gemini} and the {half-baked
knightship}s, are stationary throughout almost all of their life
cycles, as they construct the necessary mechanisms to support a
sudden short move. The waterbear constructs support for {(23,5)c/79}
{reburnable fuse} reactions which are in constant motion.
:wave: A wick-like structure attached at both ends to moving
spaceship-like patterns, in such a way that the entire pattern is
mobile. If the wave gets longer over time, the supporting patterns
are {wavestretcher}s.
Also, the gliders or spaceships emitted by a rake may be referred
to as a wave, again because the line as a whole appears to move in a
different direction from the individual components, due to the rake's
movement. Compare with {stream}.
In general a wave can be interpreted as moving at a variety of
different velocities, depending on which specific subcomponents are
chosen as the starting and ending points for calculating speed and
direction. See {antstretcher}, {wavestretcher} for a practical
example of identical wave ends being connected to spaceships with
different velocities.
:wavefront: (p4) Found by Dave Buckingham, 1976 or earlier.
........**...
........*....
.........*...
........**...
.....**...**.
....*..***..*
....*.....**.
.....*...*...
**.*.*...*...
*.**.*.**....
....*.*......
....*.*......
.....*.......
:waveguide: = {superstring}.
:wavestretcher: A {spaceship} pattern that supports a connection to an
extensible periodic {wick}-like structure, whose speed and/or
direction of propagation are different from those of the
wavestretcher spaceship.
Connecting the following to a standard diagonal {antstretcher}
creates a new oblique {wavestretcher} (a type of {growing spaceship})
and also an alternate {space nonfiller} mechanism.
.......................................................*.....
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**......................*.***....*......................*...*
..**.**.................*..*....*....................*...*...
..**...**.**...............*..*................**.*...*.****.
**.....**...**.**.........**.***...**..**.***.*....*.....*..*
.....**.....**...**.**......*.**..*.*..***.**.*.*...*......*.
..........**.....**...**.*...*....*.*.*..**..*..*...****.....
...............**.....**..*.*.**..*..*.......................
....................**...........*....*..........**...**.....
.......................................*..........*..........
....................................*........................
....................................**.......................
A required supporting c/5 {spark} is shown at the right edge. It can
be supplied by a {spider} or another c/5 orthogonal spaceship with a
similar {edge spark}. Alternatively, the c/5 component could
theoretically be replaced by a supporting spaceship traveling
diagonally at c/6, to support the same oblique trail of ants. As of
August 2017 no workable c/6 component has been found.
:wedge: A 26-cell quadratic growth pattern found by Nick Gotts in March
2006, based on {Gotts dots}. In terms of its initial population,
this is the smallest known pattern with superlinear growth.
:wedge grow: = {wedge}.
:weekender: (2c/7 orthogonally, p7) Found by David Eppstein in January
2000. In April 2000 Stephen Silver found a tagalong for a pair of
weekenders. At present, n weekenders pulling n-1 tagalongs
constitute the only known {spaceship}s of this speed or period,
except for variants of the {weekender distaff} that suppress its
output gliders.
.*............*.
.*............*.
*.*..........*.*
.*............*.
.*............*.
..*...****...*..
......****......
..****....****..
................
....*......*....
.....**..**.....
:weekender distaff: (2c/7, p16982) The first orthogonal 2c/7 rake,
constructed by Ivan Fomichev on May 22nd, 2014. It uses the weak
{spark}s from {weekender}s to perturb an LWSS into an active reaction
in a variable-period loop, which produces a series of {slow salvo}
gliders that finally rebuilds the LWSS.
:weld: To join two or more {still life}s or {oscillator}s together.
This is often done in order to fit the objects into a smaller space
than would otherwise be possible. The simplest useful example is
probably the {integral sign}, which can be considered as a pair of
welded {eater1}s.
:Wheels, Life, and other Mathematical Amusements: One of Martin
Gardner's books (1983) that collects together material from his
column in Scientific American. The last three chapters of this book
contain all the Life stuff.
:why not: (p2) Found by Dave Buckingham, July 1977.
...*...
...*.*.
.*.....
*.*****
.*.....
...*.*.
...*...
:wick: A stable or oscillating linearly repeating pattern that can be
made to burn at one end. See {fuse}.
:wickstretcher: A {spaceship}-like object which stretches a {wick} that
is fixed at the other end. The wick here is assumed to be in some
sense connected, otherwise most {puffer}s would qualify as
wickstretchers. The first example of a wickstretcher was found in
October 1992 (front end by Hartmut Holzwart and back end by Dean
Hickerson) and stretches {ants} at a speed of c/4. This is shown
below with an improved back end found by Hickerson the following
month.
.................**..............................
.............**....*.............................
............***.*................................
*.**..**...*...****.*.*....**.......**...........
*....**..*........*.***....*....**.*..*.**.*.....
*.**....**.**....*...........*...*.*.**.*.**.....
......*.......*.............**.....*..*.*...**...
.....*.........*.*....***...*....*..*.*.***...*..
.....*.........*.*....***.**.*..**.*.*...*..**.*.
......*.......*.............**.*...**....**....*.
*.**....**.**....*..........*........**.*.*.**.**
*....**..*........*.***........*...*...**.*..*.*.
*.**..**...*...****.*.*.......*.*...**....*..*.*.
............***.*..............*.....*.***....*..
.............**....*.................*.*.........
.................**...................*..........
Diagonally moving c/4 and c/12 wickstretchers have also been built:
see {tubstretcher} and {linestretcher}. In July 2000 Jason Summers
constructed a c/2 wickstretcher, stretching a p50 {traffic jam} wick,
based on an earlier (October 1994) pattern by Hickerson.
:wicktrailer: Any {extensible} {tagalong}, that is, one which can be
attached to the back of itself, as well as to the back of a
{spaceship}. The number of generations which it takes for the
tagalong to occur again in the same place is often called the period
of the wicktrailer - this has little relation to the period of the
tagalong units themselves.
:windmill: (p4) Found by Dean Hickerson, November 1989.
...........*......
.........**.*.....
.......**.........
..........**......
.......***........
..................
***...............
...**..***.**.....
..........*******.
.*******..........
.....**.***..**...
...............***
..................
........***.......
......**..........
.........**.......
.....*.**.........
......*...........
:wing: The following {induction coil}. This is generation 2 of {block
and glider}.
.**.
*..*
.*.*
..**
:WinLifeSearch: Jason Summers' GUI version of {lifesrc} for MS Windows.
It is available from {http://entropymine.com/jason/life/software/}.
:Winning Ways: A two-volume book (1982) by Elwyn Berlekamp, John Conway
and Richard Guy on mathematical games. The last chapter of the
second volume concerns Life, and outlines a proof of the existence of
a {universal constructor}.
:wire: a repeating stable structure, usually fairly dense, that a
{signal} can travel along without making any permanent change. Known
wires are the diagonal {2c/3 wire}, and {lightspeed telegraph} wire
made from an orthogonal chain of beehives.
:with the grain: term used for {negative spaceship}s traveling in
{zebra stripes} agar, parallel to the stripes, and also for
{with-the-grain grey ship}s.
Below are three small examples of "negative spaceships" found by
Gabriel Nivasch in July 1999, traveling with the grain through a
stabilized finite segment of zebra stripes agar:
.*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*.
.****************************************************.
......................................................
.****************************************************.
*....................................................*
.****************************************************.
................................................*.....
.****************************************.****....***.
*.........................................**.....*...*
.**************************************.....*********.
.............................................*........
.************************************.........**..***.
*.....................................*.*.....**.*...*
.************************************...*.....***.***.
.............................................*........
.**************************************.....*********.
*.........................................**.....*...*
.****************************************.****....***.
................................................*.....
.****************************************************.
*....................................................*
.****************************************************.
......................................................
.*************************..***..***..***..**********.
*..........................**...**...**...**..*......*
.***********************...*....*....*....*.....*****.
...........................**...**...**...**...*......
.*************************..***..***..***..**********.
*....................................................*
.****************************************************.
......................................................
.****************************************************.
*....................................................*
.****************************************************.
......................................................
.***********************..***..***..***..***..*******.
*........................**...**...**...**...**......*
.***********************...**...**...**...**...******.
................................................*.....
.*********************...........................****.
*................................................*...*
.*********************...........................****.
................................................*.....
.***********************...**...**...**...**...******.
*........................**...**...**...**...**......*
.***********************..***..***..***..***..*******.
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.****************************************************.
*....................................................*
.****************************************************.
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.****************************************************.
.*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*..*.
It has been proven that signals traveling non-destructively with the
grain through zebra stripes cannot travel at less than the {speed of
light}.
:with-the-grain grey ship: A {grey ship} in which the region of density
1/2 consists of lines of ON cells lying parallel to the direction in
which the spaceship moves. See also {against-the-grain grey ship}.
:WLS: = {WinLifeSearch}
:worker bee: (p9) Found by Dave Buckingham in 1972. Unlike the similar
{snacker} this produces no {spark}s, and so is not very important.
Like the snacker, the worker bee is {extensible} - it is, in fact, a
finite version of the infinite oscillator which consists of six ON
cells and two OFF cells alternating along a line. Note that Dean
Hickerson's new snacker ends also work here.
**............**
.*............*.
.*.*........*.*.
..**........**..
................
.....******.....
................
..**........**..
.*.*........*.*.
.*............*.
**............**
:W-pentomino: Conway's name for the following {pentomino}, a common
{loaf} {predecessor}.
*..
**.
.**
:*WSS: Any of the standard orthogonal spaceships -- {LWSS}, {MWSS}, or
{HWSS}.
:x66: (c/2 orthogonally, p4) Found by Hartmut Holzwart, July 1992. Half
of this can be escorted by a HWSS. The name refers to the fact that
every cell (live or dead) has at most 6 live neighbours (in contrast
to {spaceship}s based on {LWSS}, {MWSS} or {HWSS}). In fact this
spaceship was found by a search with this restriction.
..*......
**.......
*..***..*
*....***.
.***..**.
.........
.***..**.
*....***.
*..***..*
**.......
..*......
:Xlife: A popular freeware Life program that runs under the X Window
System. The main Life code was written by Jon Bennett, and the X
code by Chuck Silvers.
:X-pentomino: Conway's name for the following {pentomino}, a {traffic
light} {predecessor}.
.*.
***
.*.
:Y-pentomino: Conway's name for the following {pentomino}, which
rapidly dies.
..*.
****
:Z-hexomino: The following {hexomino}. The Z-hexomino features in the
{pentoad}, and also in {Achim's p144}.
**.
.*.
.*.
.**
:zone of influence: The set of cells on which a chosen cell or pattern
can potentially exert an influence in a given number of generations
N. If N is not specified it is generally taken to be one, in which
case the zone of influence simply coincides with the Moore
neighbourhood of the cell or pattern.
The set for N generations consists of all the cells to which at least N
paths of length N can be traced from the cell(s) in question.
Contrast this with the range-N Moore neighbourhood, which consists of
all cells to which at least one path of length n can be traced.
:zebra stripes: (p1) A stable agar consisting of alternating bands of
live and dead cells. This is the pattern that known {spacefiller}s
and many {gray ship}s create. It is also the medium through which
{with the grain} and {against the grain} {negative spaceship}s
travel. Many simple stabilizations of the boundaries of finite
regions of this agar are known.
..**.......................
..*........................
....*..*..*..*..*..*..*....
...********************....
..*........................
...******************......
.....................*.....
.********************......
*..........................
.**********************....
.......................*.**
.********************..*.**
*....................*.*...
.********************..*...
.......................**..
...******************......
..*..................*.....
...******************......
...........................
.....**..**.*.****.**......
.....**..*.**.*..*.**......
:Z-pentomino: Conway's name for the following {pentomino}, which
rapidly dies.
**.
.*.
.**
:zweiback: (p30) An oscillator in which two {HW volcano}es {hassle} a
{loaf}. This was found by Mark Niemiec in February 1995. A smaller
version using using Scot Ellison's reduced HW volcano is shown below.
..........*..............................
........*****.................*..........
.......*.....*..............*****........
.......*..**.*.............*.....*.......
...*.***.*.*.**............*.**..*.......
...**....*................**.*.*.***.*...
......**.**....................*....**...
.*****.*.*..*.................**.**......
*......*...*.*..............*..*.*.*****.
**..*****.**.*.............*.*...*......*
............**.............*.**.*****..**
.....**....***.............**............
.....**....***.....**......***....**.....
............**....*..*.....***....**.....
**..*****.**.*.....*.*.....**............
*......*...*.*......*......*.**.*****..**
.*****.*.*..*..............*.*...*......*
......**.**.................*..*.*.*****.
...**....*....................**.**......
...*.***.*.*.**................*....**...
.......*..**.*............**.*.*.***.*...
.......*.....*.............*.**..*.......
........*****..............*.....*.......
..........*.................*****........
..............................*..........
-----------------------------------------------------------------------
Bibliography.
David I. Bell, "Spaceships in Conway's Life". Series of articles
posted on comp.theory.cell-automata, Aug-Oct 1992. Now available
from his website (http://www.canb.auug.org.au/~dbell/).
David I. Bell, "Speed c/3 Technology in Conway's Life", 17 December
1999. Available from his website (see above).
Elwyn R. Berlekamp, John H. Conway and Richard K. Guy, "Winning Ways
for your Mathematical Plays, II: Games in Particular". Academic
Press, 1982.
David J Buckingham, "Some Facts of Life". BYTE, December 1978.
Dave Buckingham, "My Experience with B-heptominos in Oscillators".
12 October 1996. Available from Paul Callahan's website
(http://conwaylife.com/ref/lifepage/patterns/bhept/bhept.html).
David J. Buckingham and Paul B. Callahan, "Tight Bounds on Periodic Cell
Configurations in Life". Experimental Mathematics 7:3 (1998) 221-241.
Available at
https://web.archive.org/web/*/http://www.expmath.org/restricted/7/7.3/callahan.ps .
Noam D. Elkies, "The still-Life density problem and its
generalizations", pp228-253 of "Voronoi's Impact on Modern Science,
Book I", P. Engel, H. Syta (eds), Institute of Mathematics,
Kyiv 1998 = Vol.21 of Proc. Inst. Math. Nat. Acad. Sci. Ukraine,
math.CO/9905194 (http://front.math.ucdavis.edu/math.CO/9905194).
Martin Gardner, "Wheels, Life, and other Mathematical Amusements".
W. H. Freeman and Company, 1983.
R. Wm. Gosper, "Exploiting Regularities in Large Cellular Spaces".
Physica 10D (1984) 75-80.
N. M. Gotts and P. B. Callahan, "Emergent structures in sparse fields of
Conway's 'Game of Life'", in "Artificial Life VI: Proceedings of the
Sixth International Conference on Artificial Life", MIT Press, 1998.
Mark D Niemiec, "Life Algorithms". BYTE, January 1979.
William Poundstone, "The Recursive Universe". William Morrow and
Company Inc., 1985.