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

Introduction | Bibliography

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:Gabriel's p138 (p138) The following oscillator found by Gabriel Nivasch in October 2002.

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

: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. Dave Greene is also a frequent contributor to the blog, which can be found at http://gameoflife-news.blogspot.com.

: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.

    ..O.OOO.....
    OO.O.OOOOO.O
    O.O.OO.O.O..
    .OOOO.O.OOO.
    O.O.OO.OOO.O
    .OOO.OO.O.O.
    ..O...OOO..O
    .O.OO.O.O.O.
    OOO.OOOO.O.O
    OO.OOOO...O.
    .O.O.OO..O..
    .OO.O..OO.O.

:generation The fundamental unit of time. The starting pattern is generation 0.

:germ (p3) Found by Dave Buckingham, September 1972.

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

:gfind A program by David Eppstein which uses de Bruijn graphs to search for new spaceships. 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.

: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 spaceships 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 guns 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.

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

: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.)

    OOO
    O..
    .O.

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.)

    ...OO...
    ...OO...
    ........
    ........
    ..O..O..
    O.O..O.O
    .OO..OO.

: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 oscillators or by spaceships. The most useful glider duplicators are those with low periods.

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.

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

Spaceship convoys which can duplicate gliders are very useful since they (along with glider turners) 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 gliders.

:glider injection gate = GIG

:gliderless A gun is said to be gliderless if it does not use gliders. 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.

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

: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 guns where it may be necessary to produce a number of gliders travelling on close parallel paths. See also edge shooter.

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

: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.

    OO..O
    O...O
    O..OO

: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 lifes and known oscillators with at most 14 cells were found by Dave Buckingham.

Perhaps the most interesting glider syntheses are those of spaceships, because these can be used to create corresponding guns and rakes. Many of the c/2 spaceships that are based on standard spaceships have been synthesized, mostly by Mark Niemiec. In June 1998 Stephen Silver found syntheses for some of the Corderships (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 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.

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

:glider train A certain puffer that produces two rows of blocks 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 spaceships. The following diagram shows a convoy which turns a forward glider 90 degrees, with the new glider also moving forwards.

    .........OO.........
    ........OO.OOOO.....
    .O.......OOOOOO.....
    O.........OOOO......
    OOO.................
    ....................
    ....................
    ....................
    ....................
    ...O................
    .O...O..............
    O...................
    O....O..............
    OOOOO...............
    ....................
    ....................
    .............OOOOOO.
    .............O.....O
    .............O......
    ..............O....O
    ................OO..

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.

: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. It remains by far the smallest known gun. Gosper has since found other guns, see new gun and the p144 gun shown under factory.

    ........................O...........
    ......................O.O...........
    ............OO......OO............OO
    ...........O...O....OO............OO
    OO........O.....O...OO..............
    OO........O...O.OO....O.O...........
    ..........O.....O.......O...........
    ...........O...O....................
    ............OO......................

:gourmet (p32) Found by Dave Buckingham in March 1978. Compare with pi portraitor and popover.

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

: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.

    ......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......

:gray ship = grey ship

:great on-off (p2)

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

:grey counter = Gray counter (This form is erroneous, as Gray is surname, not a colour.)

:grey ship A spaceship that contains a region with a density of 1/2, and which is extensible in such a way that the region of 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.

    O..O
    .OO.

: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).

    ........OO.......
    .......OO........
    .........O.......
    ...........OO....
    ..........O......
    .................
    .........O..OO...
    .OO.....OO....O..
    OO.....O.....O...
    ..O....O.O...OO..
    ....O..O....OO.O.
    ....OO.......OO..
    ........O....O.OO
    .......O.O..O.OO.
    ........O........

: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 cleanly at a slower rate than the puffer is producing it. Examples include blinker ships and pi ships.

:gull = elevener

:gun Any stationary pattern that emits spaceships (or rakes) forever. For examples see double-barrelled, edge shooter, factory, gliderless, Gosper glider gun, new gun and true.

:gunstar Any of a series of glider guns 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).

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