:R = R-pentomino
:R190 A composite conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in July 1996. It is made up of two elementary conduits, 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:
..........OO......................... .......OO..O......................... .....OOO.OO.......................... ....O................................ .O..OOOO.OO.......................... .OOO...O.OO.......................... ....O................................ ...OO..........................OO.... ...............................O..... .............................O.O..... .............................OO...... ..................................... ..................................... ..................................... ..................................... .................................OO.O .................................O.OO ..................................... O.........................OO......... O.O.......................OO......... OOO.................................. ..O.................................. ..................................... ..................................... .........OO...OO..................... ..........O...O...................... .......OOO.....OOO................... .......O.........O................... .................O.O................. ..................OO................. ..................................... ..................................... ..................................... ..................................... ..................................... .........................OOO......... .........................O........... ........................OO...........
: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.
.....O..... ....O.O.... ...O.O.O... ...O.O.O... OO.O...O.OO OO.O...O.OO ...O...O... ...O.O.O... ....O.O.... .....O.....
:r5 = R-pentomino
:R64 An elementary conduit, one of the original sixteen Herschel conduits, 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:
..........OO........... ..........OO.....OO.... .................OO.... ....................... ....................... ...............OO...... ...............OO...... .....................OO .....................OO ....................... ....................... ....................... .O..................... .O.O................... .OOO................... ...O................... ....................... ....................... ....................... ...OO.OO............... ..O.O.O.O.............. ..O.O..O............... .OO.O........OOO....... O...OO.......O......... .O.O..O.O...OO......... OO.OO..OO..............R64 is one of the simplest known Spartan conduits, one of the two known Blockic conduits, and one of the few elementary conduits in the original set of sixteen. See also p256 gun.
:rabbits (stabilizes at time 17331) A 9-cell methuselah found by Andrew Trevorrow in 1986.
O...OOO OOO..O. .O.....The following predecessor, found by Trevorrow in October 1995, has the same number of cells and lasts two generations longer.
..O....O OO...... .OO.OOO.
:racetrack A pattern in which a signal makes its way in a loop through an "obstacle course" of reactions in order to demonstrate various ways that the signal can be reflected, temporarily stored, and converted. The more different reactions that are used the better the racetrack. David Goodenough built racetracks for p30 and p46 technology in 1995. Racetracks are also known for Herschel conduit technology, and simple ones are useful for building oscillators and glider guns.
:rake Any puffer whose debris consists of spaceships. 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 Corderships 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' backrake, March 2001).
:$rats (p6) Found by Dave Buckingham, 1972.
.....OO..... ......O..... ....O....... OO.O.OOOO... OO.O.....O.O ...O..OOO.OO ...O....O... ....OOO.O... .......O.... ......O..... ......OO....
: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 cells that are alive during some part of a given active reaction. This term is used for Herschel circuits 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.
:reanimation A reaction performed by a convoy of spaceships (or other moving objects) which converts a common stationary object into gliders without harming the convoy. This provides one way for signals that have been frozen in place by some previous reaction to be released for use.
Simple reactions using period 4 c/2 spaceships have been found for reanimating a block, boat, beehive, ship, loaf, bi-block, or toad. The most interesting of these is for a beehive since it seems to require an unusual p4 spaceship:
..........O....................... .........O.O...................... .........O.O...................... ..........O....................... .................................. ...............OOO.............OOO ..............O..O.....OOO....O..O .................O....O..O.......O .............O...O....O...O..O...O .................O..O...O.O......O ..OOO............O.O........OO..O. .O..O..............O........OOOOO. ....O..........OOO...O......OO.... O...O..........................OO. O...O............................. ....O............................. .O.O...............O.............. ..................OOO............. .................OO.O............. ....O............OOO.............. ...OOO...........OOO.............. ...O.OO..........OOO.............. ....OOO...........OO.............. ....OOO........................... ....OO............................
Reanimation of a loaf is used many times in the Caterloopillar. It is also used in the Caterpillar as part of its catch and throw mechanism. Finally, reanimation can produce rakes from some puffers. See stop and restart for a similar idea that applies to Herschel conduits and other signal circuitry.
There are small objects which have no known reanimation reactions using c/2 ships other than the brute force method of hitting them with the output of rakes.
:reburnable fuse A very rare type of fuse whose output is identical to its input, possibly with some spatial and/or temporal offset. See lightspeed wire for an example. Reburnable fuses are used primarily in the construction of fixed-speed self-supporting macro-spaceships, 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.
:recipe = glider synthesis or construction recipe.
: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 oscillators with previously unknown periods, 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.
..O......................................... O.O......................................... .OO......................................... ............................................ ..............O............................. .............O.O............................ .............O.O............................ ..............O............................. ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ ............................................ .......................OO................... .......................OO................... ............................................ .....OO..................................... ....O.O..................................... ....O....................................... ...OO....................................... ..................................OO........ .................................O..O..OO... .................................O.O....O... ..............OO..................O.....O.OO .............O.O.....................OO.O.O. .............O.......................O..O..O ............OO....................O....O..OO ..................................OOOOO..... ............................................ ....................................OO.O.... ....................................O.OO.... ............................OOO............. ............................O............... .............................O..............
: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 and 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 guns can also be made into reflectors, although these are mostly rather large.
In September 1998 Noam Elkies found some fast small-period glider reflectors, with oscillators supplying the required domino sparks at different periods. A figure-8 produced a p8 reflector, and a p6 pipsquirter produced an equivalent p6 reflector. A more complicated construction allows a p5 reflector (which, as had been anticipated, soon led to a true p55 Quetzal gun). And in August 1999 Elkies found a suitable sparker to produce a p7 reflector, allowing the first p49 oscillator to be constructed.
On 6 April 2016, Tanner Jacobi discovered an equally small and simple reaction, the bumper, starting with a loaf as bait instead of a boat. This resulted in a series of periodic colour-preserving reflectors, whereas Elkies' reflectors are all colour-changing.
Stable reflectors are special in that if they satisfy certain conditions they can be used to construct oscillators 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.
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.
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 Dieter 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 colour-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 colour-changing stable reflector contained within a 25 by 25 bounding box, with a recovery time of 50 generations or less.
See also rectifier, glider turner.
:reflectorless rotating oscillator A pattern that rotates itself 90 or 180 degrees after some number of generations, with the additional constraint that multiple non-interacting copies of the pattern can be combined into a new oscillator with a period equal to the appropriate fraction of the component oscillators' period. The second constraint disqualifies small time-symmetric oscillators such as the blinker and monogram.
A working RRO might look something like a pi orbital or p256 gun loop containing one or more pis or Herschels in the same loop, but without any external stabilisation mechanism. Such patterns can be proven to exist (see universal constructor), but as of October 2017 none have been explicitly constructed in Life. There is no upper limit on multiplicity for a constructor-based RRO.
:regulator An object which converts input gliders 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.
:relay Any oscillator in which spaceships (typically gliders) travel in a loop. The simplest example is the p60 one shown below using two pentadecathlons. 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.
...........................O....O.. ................OO.......OO.OOOO.OO .................OO........O....O.. ................O.................. ..O....O........................... OO.OOOO.OO......................... ..O....O...........................
: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 reflectors or conduits where the signal objects (gliders or Herschels, 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, glider-block cycle, that reflects the gliders 180 degrees.
..O..O.. O.O..O.O .OO..OO. ........ ........ ...OO... ...OO...
: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. The 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 replicates itself only once, allowing no possibility of superlinear growth.
:reverse fuse A fuse that produces some initial debris, but then burns cleanly. The following is a simple example.
.............OO ............O.O ...........O... ..........O.... .........O..... ........O...... .......O....... ......O........ .....O......... ....O.......... ...O........... ..O............ OO.............
:revolver (p2)
O............O OOO....O...OOO ...O.O.O..O... ..O......O.O.. ..O.O......O.. ...O..O.O.O... OOO...O....OOO O............O
:Rich's p16 A period 16 oscillator found by Rich Holmes in July 2016, using apgsearch. For its use as a filter see for example p48 gun.
....O...O.... ..OO.O.O.OO.. .O...O.O...O. O...OO.OO...O O.O.......O.O .O.........O. ............. ....OO.OO.... ...O.O.O.O... ....O...O....
:ring of fire (p2) The following muttering moat found by Dean Hickerson in September 1992.
................O................. ..............O.O.O............... ............O.O.O.O.O............. ..........O.O.O.O.O.O.O........... ........O.O.O..OO.O.O.O.O......... ......O.O.O.O......O..O.O.O....... ....O.O.O..O..........O.O.O.O..... .....OO.O..............O..O.O.O... ...O...O..................O.OO.... ....OOO....................O...O.. ..O.........................OOO... ...OO...........................O. .O...O........................OO.. ..OOOO.......................O...O O.............................OOO. .OOO.............................O O...O.......................OOOO.. ..OO........................O...O. .O...........................OO... ...OOO.........................O.. ..O...O....................OOO.... ....OO.O..................O...O... ...O.O.O..O..............O.OO..... .....O.O.O.O..........O..O.O.O.... .......O.O.O..O......O.O.O.O...... .........O.O.O.O.OO..O.O.O........ ...........O.O.O.O.O.O.O.......... .............O.O.O.O.O............ ...............O.O.O.............. .................O................
: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 patterns in Conway's Life and other similar cellular automata. This encoding was introduced by Dave Buckingham and is now the usual means of exchanging relatively small patterns by email or in online forum discussions.
As an example of the rle format, here is a representation of the Gosper glider gun. The "run lengths" are the numbers, b's are dead cells, o's are live cells, and dollar signs signal new lines:
x = 36, y = 9, rule = B3/S23 24bo$22bobo$12boo6boo12boo$11bo3bo4boo12boo$oo8bo 5bo3boo$oo8bo3boboo4bobo$10bo5bo7bo$11bo3bo$12boo!
Over the years RLE format has been extended to handle patterns with multiple states, neighborhoods, rules, and universe sizes. A completely different encoding, macrocell format, is used for repetitive patterns that may have very large populations.
: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. See also multiple roteightors.
.O............ .OOO........OO ....O.......O. ...OO.....O.O. ..........OO.. .............. .....OOO...... .....O..O..... .....O........ ..OO..O...O... .O.O......O... .O.......O.... OO........OOO. ............O.
: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 gliders.
.OO OO. .O.At generation 774, an R-pentomino produces a queen bee which lasts 17 more generations before being destroyed, enough time for it to flip over. This observation led to the discovery of the Gosper glider gun.
:RRO = reflectorless rotating oscillator
: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.
..............OO......OO......OO...O.OO.......... ....O........O..O....O..O....O..O..OO.O.......... O..O.O....O...OO..O...OO..O...O.O.....O.OO....... OOOO.O..OOOOOO..OOOOOO..OOOOOO..OOOOOO.O.O....... .....O.O.....O.O.....O.O.....O.O.....O.O......OO. ..OO.O.O.O.O...O.O.O...O.O.O...O.O.O...O.O.....O. .O.....O.O...O.O.O...O.O.O...O.O.O...O.O.O.O.OO.. .OO......O.O.....O.O.....O.O.....O.O.....O.O..... .......O.O.OOOOOO..OOOOOO..OOOOOO..OOOOOO..O.OOOO .......OO.O.....O.O...O..OO...O..OO...O....O.O..O ..........O.OO..O..O....O..O....O..O........O.... ..........OO.O...OO......OO......OO..............
:Rx202 A composite conduit, one of the original sixteen Herschel conduits, discovered by Dave Buckingham in May 1997. It is made up of two elementary conduits, 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:
..............OO............... ...........OO..O............... .........OOO.OO......O......... ........O..........OOO......... .........OOO.OO...O............ ...........O.OO...OO........... ............................... ............................... ............................... ............................... .......................OO...... .......................O....... .....................O.O....... .....................OO........ ............................... ............................... ............................... ............................... ............................... ...O........................... ...O.O......................... ...OOO......................... .....O......................... ......................OO....... ......................OO....... ............................... ............................... ............................... ............................... ............................... ............................... ............................... O.OO........................... OO.O........................... .....................OO........ .........OO.........O..O..OO... .........OO.........O.O....O... .....................O.....O.OO ........................OO.O.O. ........................O..O..O .....................O....O..OO .....................OOOOO..... ............................... ...................OOOOOOO..... ...................O..O..O..... .................O.O........... .................OO............ ............................... ............................... ............................... ............................... ............................... .........OOO................... ...........O................... ...........OO..................