Life Lexicon (R)
Author: Stephen A. Silver
Description: Part of Stephen Silver's Life Lexicon.

Introduction | Bibliography

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:R = R-pentomino

: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 discovered 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

: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.

: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, March 2001) - see backrake.

:$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

:receiver See Herschel receiver.

: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. 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.

    ......OO.....OO..
    O.O...OO.....O...
    .OO........O.O...
    .O.........OO....
    .......OO........
    .......O.O.......
    ........O........
    .................
    ...........OOO...
    ...........OOO...
    ...........OOO...
    ..............OOO
    ..............OOO
    ..............OOO

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.

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 also won the $100 prize that Dieter Leithner had offered in April 1997 for the first stable reflector to fit in a 50x50 box, and the additional $100 that Alan Hensel had offered in January 1999 for the same feat. Dave Greene has subsequently offered $50 for the first 90-degree stable glider reflector that fits in a 50x50 box, and a further $50 for the first in a 35x35 box.

See also glider turner.

: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.

: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 and the objects (gliders or Herschels, for example) will interact fatally with each other (or one will interact fatally with a disturbance caused by the other) if they are too close together. 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.

    ..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.

: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

: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 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 (especially large ones) by e-mail.

: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.

    .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.

    .OO
    OO.
    .O.

: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..............

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