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Life Lexicon
Release 25, 2006 February 28
Multipage HTML version
http://www.argentum.freeserve.co.uk/lex_home.htm
INTRODUCTION
This is a lexicon of terms relating to John Horton Conway's Game of Life. It is also available in asingle-page HTML version and an ASCII version.
This lexicon was compiled by Stephen A. Silver - see below for additional credits. See my web-site
for contact information.
The latest versions of this lexicon (both HTML and ASCII) should be available from the LifeLexicon Home Page.
CREDITS
The largest single source for the early versions of this lexicon was a glossary compiled by AlanHensel "with indispensable help from John Conway, Dean Hickerson, David Bell, Bill Gosper, BobWainwright, 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 aspattern 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 DeanHickerson's header to his 1995 stamp file.
Most of the information on recent results is from the discoverers themselves.
The following people all provided useful comments on earlier releases of this lexicon: David Bell,Nicolay Beluchenko, Johan Bontes, Scot Ellison, Nick Gotts, Dave Greene, Alan Hensel, DeanHickerson, Dieter Leithner, Mark Niemiec, Gabriel Nivasch, Andrew Okrasinski, Peter Rott, KenTakusagawa, Andrew Trevorrow and Malcolm Tyrrell.
The format, errors, use of British English and anything else you might want to complain about are
by Stephen Silver.COPYING
This lexicon is copyright Stephen Silver, 1997-2005. It may be freely copied and/or modified aslong as due credit is given. This includes not just credit to those who have contributed in some wayto the present version (see above), but also credit to those who have made any modifications.
LEXICOGRAPHICORDER
I have adopted the following convention: all characters (including spaces) other than letters anddigits are ignored for the purposes of ordering the entries in this lexicon. (Many terms are used bysome people as a single word, with or without a hyphen, and by others as two words. Myconvention means that I do not have to list these in two separate places. Indeed, I list them onlyonce, choosing whichever form seems most common or sensible.) Digits lexicographically precede
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letters.
FORMAT
The diagrams in this lexicon are in a very standard format. You should be able to simply copy apattern, paste it into a new file and run it in your favourite Life program. If you use Johan Bontes'Life32, Mirek Wjtowicz' MCell or Andrew Trevorrow and Tomas Rokicki's Golly then you can
just paste the pattern directly into the Life program. I have restricted myself to diagrams of size6464 or less.
Most definitions that have a diagram have also some data in brackets after the keyword. Oscillatorsare maked as pn (where n is a positive integer), meaning that the period is n (p1 indicates a stilllife). 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 withspeed and period and have the word "fuse" added. Wicks and fuses are infinite in extent and so havenecessarily 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 issimilar to Life, but has a tiny replicator) and Day & Night (which is very different, but exhibitsmany of the same phenomena). These articles can be found on his web-site.
ERRORSANDOMISSIONS
If you find any errors (including typos) or serious omissions, then please let me know.
NAMES
When deciding whether to use full or abbreviated forms of forenames I have tried, whereverpossible, to follow the usage of the person concerned.
QUOTEEvery 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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: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.
....OO......OO....
...O.O......O.O...
...O..........O...
OO.O..........O.OO
OO.O.O..OO..O.O.OO
...O.O.O..O.O.O...
...O.O.O..O.O.O...
OO.O.O..OO..O.O.OO
OO.O..........O.OO
...O..........O...
...O.O......O.O...
....OO......OO....
:1-2-3 (p3) Found by Dave Buckingham, August 1972. This is one of only three essentially differentp3 oscillators with only three cells in the rotor. The others are stillater and cuphook.
..OO......
O..O......
OO.O.OO...
.O.O..O...
.O....O.OO
..OOO.O.OO
.....O....
....O.....
....OO....
:1-2-3-4 (p4) See also Achim's p4.
.....O.....
....O.O....
...O.O.O...
...O...O...
OO.O.O.O.OO
O.O.....O.O
...OOOOO...
...........
.....O.....
....O.O....
.....O.....
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:14-ner = fourteener
:2 eaters = two eaters
:4-8-12 diamond The following pure glider generator.
....OOOO....
............
..OOOOOOOO..
............
OOOOOOOOOOOO
............
..OOOOOOOO..
............
....OOOO....
:4 boats (p2)
...O....
..O.O...
.O.OO...
O.O..OO.
.OO..O.O
...OO.O.
...O.O..
....O...
:4F = Fast Forward Force Field
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:Achim's p144 (p144) This was found (minus the blocks shown below) on a cylinder of width 22by Achim Flammenkamp in July 1994. Dean Hickerson reduced it to a finite form using figure-8sthe 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.
OO........................OO
OO........................OO
..................OO........
.................O..O.......
..................OO........
..............O.............
.............O.O............
............O...O...........
............O..O............
............................
............O..O............
...........O...O............
............O.O.............
.............O..............
........OO..................
.......O..O.................
........OO..................
OO........................OO
OO........................OO
:Achim's p16 (p16) Found by Achim Flammenkamp, July 1994.
.......OO....
.......O.O...
..O....O.OO..
.OO.....O....
O..O.........
OOO..........
.............
..........OOO
.........O..O
....O.....OO.
..OO.O....O..
...O.O.......
....OO.......
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:Achim's p4 (p4) Dave Buckingham found this in a less compact form (using two halves ofsombreros) in 1976. The form shown here was found by Achim Flammenkamp in 1988. The rotor istwo copies of the rotor of 1-2-3-4, so the oscillator is sometimes called the "dual 1-2-3-4".
..OO...OO..
.O..O.O..O.
.O.OO.OO.O.OO.......OO
..O.O.O.O..
OO.......OO
.O.OO.OO.O.
.O..O.O..O.
..OO...OO..
:Achim's p5 = pseudo-barberpole
:Achim's p8 (p8) Found by Achim Flammenkamp, July 1994.
.OO......
O........
.O...O...
.O...OO..
...O.O...
..OO...O.
...O...O.
........O
......OO.
:acorn (stabilizes at time 5206) A methuselah found by Charles Corderman.
.O.....
...O...
OO..OOO
:A for all (p6) Found by Dean Hickerson in March 1993.
....OO....
...O..O...
...OOOO...
.O.O..O.O.
O........O
O........O
.O.O..O.O.
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...OOOO...
...O..O...
....OO....
: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-graingrey 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 spacefillers. For some more examples seechicken wire, houndstooth agar, onion rings, squaredance and Venetian blinds. Tiling the plane withthe pattern O......O produces another interesting example: a p6 agar which has a phase of density3/4, 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.
OO..
O..O
..OO
:airforce (p7) Found by Dave Buckingham in 1972. The rotor consists of two copies of that used inthe burloaferimeter.
.......O......
......O.O.....
.......O......
..............
.....OOOOO....
....O.....O.OO
...O.OO...O.OO
...O.O..O.O...
OO.O...OO.O...
OO.O.....O....
....OOOOO.....
..............
......O.......
.....O.O......
......O.......
:AK47 reaction The following reaction (found by Rich Schroeppel and Dave Buckingham) inwhich 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
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pseudo) p94 glider gun found by Paul Callahan in July 1994, and was in 1990 the basis for the DeanHickerson's construction of the first true p94 gun. (This latter gun was enormous, and has now beensuperseded by comparatively small Herschel loop guns.)
.....O....
....O.O...
...O...O..
...O...O..
...O...O..
....O.O...
.....O....
..........
..OO......
...O......
OOO.....OO
O.......OO
:Al Jolson = Jolson
:almosymmetric (p2) Found in 1971.
....O....
OO..O.O..
O.O......
.......OO
.O.......
O......O.
OO.O.O...
.....O...
:anteater A pattern that consumes ants.
:antlers = moose antlers
:ants (p5 wick) The standard form is shown below. It is also possible for any ant to be displaced byone or two cells relative to either or both of its neighbouring ants. Dean Hickerson found fencepostsfor both ends of this wick in October 1992 and February 1993. See electric fence, and alsowickstretcher.
OO...OO...OO...OO...OO...OO...OO...OO...OO..
..OO...OO...OO...OO...OO...OO...OO...OO...OO
..OO...OO...OO...OO...OO...OO...OO...OO...OO
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OO...OO...OO...OO...OO...OO...OO...OO...OO..
:antstretcher Any wickstretcher that stretches ants.
:anvil The following induction coil.
.OOOO.
O....O
.OOO.O
...O.OO
:APPS (c/5 orthogonally, p30) An asymmetric PPS. The same as the SPPS, but with the two halves15 generations out of phase with one another. Found by Alan Hensel in May 1998.
:arkA pair of mutually stabilizing switch engines. The archetype is Noah's ark. The diagram belowshows an ark found by Nick Gotts that takes until generation 736692 to stabilize, and can therefore
be considered as a methuselah.
...........................O....
............................O...
.............................O..
............................O...
...........................O....
.............................OOO
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
................................
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................................
................................
OO..............................
..O.............................
..O.............................
...OOOO.........................
:arm A long extension hanging off from the main body of a spaceship or puffer perpendicular to thedirection of travel.
A lot of known spaceships have multiple arms. This is an artefact of the search methods used to findsuch spaceships, rather than an indication of what a "typical" spaceship might look like.
:ash The (stable or oscillating) debris left by a random reaction. Experiments show that for randomsoups with moderate initial densities (say 0.25 to 0.5) the resulting ash has a density of about0.0287. (This is, of course, based on what happens in finite fields. In infinite fields the situation mayconceivably be different in the long run because of the effect of certain initially very rare objectssuch as replicators.)
:aVerage (p5) Found by Dave Buckingham, 1973. The average number of live rotor cells is five(V), which is also the period.
...OO........
....OOO......
..O....O.....
.O.OOOO.O....
.O.O....O..O.
OO.OOO..O.O.O
.O.O....O..O.
.O.OOOO.O....
..O....O.....
....OOO......
...OO........
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:B = B-heptomino
:B29 (c/4 diagonally, p4) The following spaceship, found by Hartmut Holzwart in September 2004.
.......OOO.......
.......O.........
OOO......O.......
O......O.O.......
.O....OO.OOOO....
...OOOO.OOOOO.OO.
....OO.......OO.O
:B-52 bomber The following p104 double-barrelled glider gun. It uses a B-heptomino and emitsone glider every 52 generations. It was found by Noam Elkies in March 1996, except that Elkies
used blockers instead of molds, the improvement being found by David Bell later the same month..OO....................................
.OO.................O..................
...................O.O............O.O..
....................O............O.....
OO.......OO.......................O..O.
OO.O.....OO.......................O.O.O
...O.......................O.......O..O
...O.......................OO.......OO.
O..O.................OO.....O..........
.OO..................O.................
.....................OOO...............
....................................OO.
....................................OO.
.OO....................................
O..O...................................
O.O.O................O.O....OO.....OO..
.O..O.................OO....OO.....OO.O
.....O............O...O...............O
..O.O............O.O..................O
..................O................O..O
....................................OO.
:babbling brookAny oscillator whose rotor consists of a string of cells each of which is adjacent toexactly two other rotor cells, except for the endpoints which are adjacent to only one other rotorcell. Compare muttering moat. Examples include the beacon, the great on-off, the light bulb and thespark coil. The following less trivial example (by Dean Hickerson, August 1997) is the only one
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............O...
...........O....
..........O.....
.........O......
........O.......
.......O........
......O.........
.....O..........
....O...........
...O............
OOO.............
.O..............
:baker's dozen (p12) A loaf hassled by two blocks and two caterers. The original form (using p4and p6 oscillators to do the hassling) was found by Robert Wainwright in August 1989.
OO.........OO..........
OOOO.O.....OO..........
O.O..OOO...............
...........O...........
....OO....O.O..........
....O.....O..O....O....
...........OO....OO....
.......................
...............OOO..O.O
..........OO.....O.OOOO
..........OO.........OO
:bakery (p1) A common formation of two bi-loaves.
....OO....
...O..O...
...O.O....
.OO.O...O.
O..O...O.O
O.O...O..O
.O...O.OO.
....O.O...
...O..O...
....OO....
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: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 sequenceof 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/orrotation/reflection.
:barberpole intersection = quad
:barber's pole = barberpole
:barge (p1)
.O..
O.O.
.O.O
..O.
:basic shuttle = queen bee shuttle
:beacon (p2) The third most common oscillator. Found by Conway, March 1970.
OO..
O...
...O
..OO
:beacon maker (c p8 fuse)
..............OO
.............O.O
............O...
...........O....
..........O.....
.........O......
........O.......
.......O........
......O.........
.....O..........
....O...........
...O............
OOO.............
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..O.............
..O.............
:beehive (p1) The second most common still life.
.OO.
O..O
.OO.
:beehive and dock(p1)
...OO.
..O..O
...OO.
......
.OOOO.
O....O
OO..OO
:beehive on big table = beehive and dock
:beehive pusher = hivenudger
:beehive with tail (p1)
.OO...
O..O..
.OO.O.
....O.
....OO
:belly sparkThe 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.
.O........O.
O.O......O.O
.O.OO..OO.O.
....O..O....
....O..O....
:B-heptomino (stabilizes at time 148) This is a very common pattern. It often arises with the cell at
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top left shifted one space to the left, which does not affect the subsequent evolution. B-heptominoesacquired particular importance in 1996 due to Dave Buckingham's work on B tracks - see in
particular My Experience with B-heptominos in Oscillators.
O.OO
OOO.
.O..
:B-heptomino shuttle = twin bees shuttle
:bi-block(p1) The smallest pseudo still life.
OO.OO
OO.OO
:bi-boat = boat-tie
:biclockThe following pure glider generator consisting of two clocks.
..O....
OO.....
..OO...
.O...O.
...OO..
.....OO
....O..
: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....OOO............
...O..OOO.........
....O.O...........
OO.......O........
O.O....O..O.......
O........OO.......
.OO...............
.O..O.....O.OO....
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.O.........OO.O...
...O.O......OO..O.
....OO.O....OO...O
........O.......O.
.......OOOO...O.O.
.......O.OO...OOOO
........O...OO.O..
.............OO...
.........O.OOO....
..........O..O....
:big S (p1)
....OO.
...O..O
...O.OO
OO.O...
O..O...
.OO....
: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, pressurecooker and scrubber.
:bi-loafThis term has been used in at least three different senses. A bi-loaf can be half a bakery:
.O.....
O.O....
O..O...
.OO.O..
...O.O.
...O..O
....OO.
or it can be the following much less common still life:
..O....
.O.O...
O..O...
.OO.OO.
...O..O
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...O.O.
....O..
or the following pure glider generator:
..O.
.O.O
O..O
.OO.
O..O
O.O.
.O..
:bipole (p2) The barberpole of length 2.
OO...
O.O..
.....
..O.O
...OO
:bi-pond (p1)
.OO....
O..O...
O..O...
.OO.OO.
...O..O
...O..O
....OO.
:bi-ship = ship-tie
:bit A live cell.
:biting off more than they can chew (p3) Found by Peter Raynham, July 1972.
O...........
OOO.........
...O........
..OO........
...OO.......
....OO......
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...O..O.....
...O..OO....
....OO.OOO..
........O.O.
..........O.
..........OO
:Black&White = Immigration
:blasting cap The pi-heptomino (after the shape at generation 1). A term used at MIT and stilloccasionally encountered.
:blinker (p2) The smallest and most common oscillator. Found by Conway, March 1970.
OOO
:blinker puffer Any puffer whose output is blinkers. However, the term is particularly used for p8c/2 puffers. The first such blinker puffer was found by Robert Wainwright in 1984, and wasunexpectedly simple:
...O.....
.O...O...
O........
O....O...
OOOOO....
.........
.........
.........
.OO......
OO.OOO...
.OOOO....
..OO.....
.........
.....OO..
...O....O
..O......
..O.....O
..OOOOOO.
Since then many more blinker puffers have been found. The following one was found by David Bellin 1992 when he was trying to extend an x66:
.............OOO.
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............OOOOO
...........OO.OOO
............OO...
.................
.................
.........O.O.....
..O.....O..O.....
.OOOOO...O.O.....
OO...OO.OO.......
.O.......O.......
..OO..O..O.......
..........O......
..OO..O..O.......
.O.......O.......OO...OO.OO.......
.OOOOO...O.O.....
..O.....O..O.....
.........O.O.....
.................
.................
............OO...
...........OO.OOO
............OOOOO
.............OOO.
The importance of this larger blinker puffer (and others like it), is that the engine which producesthe 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 phasechange in the puffer. This fact allows p8 blinker puffers to be used to construct rakes of all periodswhich are large multiples of four.
:blinkers bit pole (p2) Found by Robert Wainwright, June 1977.
.....OO
OOO.O.O
.......
.O.O..O
O....O.
OO...O.
:blinker ship A growing spaceship in which the wick consists of a line of blinkers. An example by
Paul Schick based on his Schick engine is shown below. Here the front part is p12 and moves at c/2,
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while the back part is p26 and moves at 6c/13. Every 156 generations 13 blinkers are created and 12are destroyed, so the wick becomes one blinker longer.
..........OOOO.............
..........O...O............
..........O................
.OO........O..O............
OO.OO......................
.OOOO...O..................
..OO...O.OO........O....OOO
......O...O........O....O.O
..OO...O.OO........O....OOO
.OOOO...O..................
OO.OO......................
.OO........O..O............
..........O................
..........O...O............
..........OOOO.............
:block(p1) The most common still life.
OO
OO
:blockade (p1) A common formation of four blocks. The final form of lumps of muck.
OO.....................
OO.....................
.......................
.......................
.OO.................OO.
.OO.................OO.
.......................
.......................
.....................OO
.....................OO
:block and dock(p1)
...OO.
...OO.
......
.OOOO.
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O....O
OO..OO
:block and glider (stabilizes at time 106)
OO..
O.O.
..OO
:blocker (p8) Found by Robert Wainwright. See also filter.
......O.O.
.....O....
OO..O....O
OO.O..O.OO
....OO....
:block on big table = block and dock
:block on table (p1)
..OO
..OO
....
OOOO
O..O
:block pusher A pattern emitting streams of gliders which can repeatedly push a block furtheraway. 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 howa block pusher works.
...................O.O
...................OO.
....................O.
......................
......................
......................
...O..................
..O...................
..OOO.................
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......................
......................
......................
......................
OO...O................
OO...O.O..............
.....OO...............
:blom (stabilizes at time 23314) The following methuselah, found by Dean Hickerson in July 2002.
O..........O
.OOOO......O
..OO.......O
..........O.
........O.O.
:blonkA block or a blinker. This term is mainly used in the context of sparse Life and was coinedby Rich Schroeppel in September 1992.
:blonker (p6) The following oscillator, found by Nicolay Beluchenko in April 2004.
O..OO....O..
OO..O.OO.O..
....O.O.....
.....OO.....
.......O....
.......O...O
.........O.O
..........O.
:boat (p1) The only 5-cell still life.
OO.
O.O
.O.
:boat-bit A binary digit represented by the presence of a boat next to a snake (or other suitableobject, 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 (inwhich case the crossing glider is deleted) or from 0 to 1 (in which case it passes unharmed). Threegliders therefore suffice for a non-destructive read. The mechanisms involved are shown in thediagram 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
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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 then the MWSS passes unharmed, but if it is 1 then the boat and the MWSS aredestroyed and, with the help of an eater1, converted into a glider which travels back along exactlythe same path that is used by the gliders that toggle the boat-bit.)
......O..................
.......O.................
.....OOO.................
.........................
.........................
.........................
.........................
.........................
.........................
.........................
................O........
..............O.O........
..........OO...OO........
...........OO............
..........O..........O.OO
.....................OO.O
.........................
.........................
.........................
.........................
.........................
.O.......................
.OO......................
O.O......................
:boat maker (c p4 fuse)
................OO
...............O.O
..............O...
.............O....
............O.....
...........O......
..........O.......
.........O........
........O.........
.......O..........
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......O...........
.....O............
OOOOO.............
....O.............
....O.............
....O.............
....O.............
: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 boats placed tip-to-tip. The name is a pun on"bow tie".
.O....
O.O...
.OO...
...OO.
...O.O
....O.
:boojum reflector (p1) Dave Greene's name for the following reflector which he found in April2001, and which is currently the smallest known stable reflector.
....O.O......OO.............................
.....OO......OO.............................
.....O......................................
............................................
............................................
............................................
............................................
............................................
............................................
........................................O...
.......................................O.O..
.......................................O.O..
....................OO................OO.OO.
....................OO......................
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......................................OO.OO.
..OO..................................OO.O..
.O.O.......................................O
.O........................................OO
OO..........................................
............................................
..................................OO........
..................................OO....OO..
...........OO...........................O.O.
..........O.O.............................O.
..........O...............................OO
.........OO.......................OO........
..................................OO........
............................................
............................................
.............................O..............
............................O.O.............
.............................O..............
:bookend The following induction coil. It is generation 1 of century.
..OO
O..O
OOO.
:bookends (p1)
OO...OO
O.O.O.O
..O.O..
.OO.OO.
:boss (p4) Found by Dave Buckingham, 1972.
.....O.....
....O.O....
....O.O....
...OO.OO...
..O.....O..
.O.O.O.O.O.
.O.O...O.O.
OO.O...O.OO
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O..O.O.O..O
..O.....O..
...OO.OO...
....O.O....
....O.O....
.....O.....
:bottle (p8) Found by Achim Flammenkamp in August 1994. The name is a back-formation fromship in a bottle.
....OO......OO....
...O..O....O..O...
...O.O......O.O...
.OO..OOO..OOO..OO.
O......O..O......OO.OO..........OO.O
.O.O..........O.O.
...OO........OO...
..................
..................
...OO........OO...
.O.O..........O.O.
O.OO..........OO.O
O......O..O......O
.OO..OOO..OOO..OO.
...O.O......O.O...
...O..O....O..O...
....OO......OO....
:bounding box The smallest rectangular array of cells that contains the whole of a given pattern.For oscillators and guns this usually is meant to include all phases 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.
.OOO.........OOO.
O.O.OO.....OO.O.O
O.O.O.......O.O.O
.O.OO.OO.OO.OO.O.
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.....O.O.O.O.....
...O.O.O.O.O.O...
..OO.O.O.O.O.OO..
..OOO..O.O..OOO..
..OO..O...O..OO..
.O....OO.OO....O.
.O.............O.
:breeder Any pattern whose population grows at a quadratic rate, although it is usual to excludespacefillers. 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 atMIT, which was the first known pattern exhibiting superlinear growth.
There are four basic types of breeder, known as MMM, MMS, MSM and SMM (where M=movingand S=stationary). Typically an MMM breeder is a rake puffer, an MMS breeder is a puffer
producing puffers which produce stationary objects (still lifes and/or oscillators), an MSM breederis a gun puffer and an SMM breeder is a rake gun. There are, however, less obvious variants ofthese types. 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 lifes (and the stator part of certain oscillators). Itindicates that the object consists of two smaller objects joined edge to edge, as in snake bridgesnake.
:broken lines A pattern constructed by Dean Hickerson in May 2005 which produces complexbroken lines of gliders and blocks.
:broth = soup
:BTC = billiard table configuration
:B track A track for B-heptominoes. The term is more-or-less synonymous with Herschel track,since a B-heptomino becomes a Herschel plus a block in twenty generations.
:buckaroo A queen bee shuttle stabilized at one end by an eater in such a way that it can turn aglider, as shown below. This was found by Dave Buckingham in the 1970s. The name is due to BillGosper.
..O.....................
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O.O.....................
.OO.....................
...........O............
.........O.O............
........O.O.............
.......O..O...........OO
........O.O...........OO
...OO....O.O............
..O.O......O............
..O.....................
.OO.....................
:bullet heptomino Generation 1 of the T-tetromino.
.O.
OOO
OOO
:bun The following induction coil. By itself this is a common predecessor of the honey farm. Seealso cis-mirrored R-bee.
.OO.
O..O
.OOO
:bunnies (stabilizes at time 17332) This is a parent of rabbits and was found independently byRobert Wainwright and Andrew Trevorrow.
O.....O.
..O...O.
..O..O.O
.O.O....
:burloaf= loaf
:burloaferimeter (p7) Found by Dave Buckingham in 1972. See also airforce.
....OO....
.....O....
....O.....
...O.OOO..
...O.O..O.
OO.O...O.O
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OO.O....O.
....OOOO..
..........
....OO....
....OO....
: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 33generations. (Compare teardrop, where the beehives are five cells closer together.)
O...
OO..
O.O.
.OOO
:by flops (p2) Found by Robert Wainwright.
...O..
.O.O..
.....O
OOOOO.
.....O
.O.O..
...O..
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:c = speed of light
:CA = cellular automaton
:caber tosser Any pattern whose population is asymptotic to c.log(t) for some constant c, and whichcontains a glider (or other spaceship) bouncing between a slower receding spaceship and a fixedreflector which emits a spaceship (in addition to the reflected one) whenever the bouncingspaceship hits it.
As the receding spaceship gets further away the bouncing spaceship takes longer to complete eachcycle, and so the extra spaceships emitted by the reflector are produced at increasingly largeintervals. More precisely, if v is the speed of the bouncing spaceship and u the speed of the recedingspaceship, then each interval is (v+u)/(v-u) times as long as the previous one. The population attime 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.
:Cambridge pulsar CP 48-56-72 = pulsar (The numbers refer to the populations of the threephases. The Life pulsar was indeed discovered at Cambridge, like the first real pulsar a few yearsearlier.)
:Canada goose (c/4 diagonally, p4) Found by Jason Summers, January 1999. It consists of a gliderplus a tagalong.
OOO..........
O.........OO.
.O......OOO.O
...OO..OO....
....O........
........O....
....OO...O...
...O.O.OO....
...O.O..O.OO.
..O....OO....
..OO.........
..OO.........
At the time of its discovery the Canada goose was the smallest known diagonal spaceship other thanthe glider, but this record has since been beaten, first by the second spaceship shown under Orion,and more recently by quarter.
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:candelabra (p3) By Charles Trawick. See also the note under cap.
....OO....OO....
.O..O......O..O.
O.O.O......O.O.O
.O..O.OOOO.O..O.
....O.O..O.O....
.....O....O.....
:candlefrobra (p3) Found by Robert Wainwright in November 1984.
.....O....
.O.OO.O.OO
O.O...O.OO
.O....O...
.....OO...
The following diagram shows that a pair of these can act in some ways like killer toads. See alsosnacker.
....O...........O....
OO.O.OO.O...O.OO.O.OO
OO.O...O.O.O.O...O.OO
...O....O...O....O...
...OO...........OO...
.....................
.....................
.........OOO.........
.........O..O........
.........O...........
.........O...O.......
.........O...O.......
.........O...........
..........O.O........
:canoe (p1)
...OO
....O
...O.
O.O..
OO...
:cap The following induction coil. It can also be easily be stabilized to form a p3 oscillator - see
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candelabra for a slight variation on this.
.OO.
O..O
OOOO
:carnival shuttle (p12) Found by Robert Wainwright in September 1984 (using MW emulators atthe end, instead of the monograms shown here).
.................................O...O
OO...OO..........................OOOOO
.O.O.O...O..O......OO...O..O.......O..
.OO.OO..OO...OO....OO..OO...OO....O.O.
.O.O.O...O..O......OO...O..O.......O..
OO...OO..........................OOOOO
.................................O...O
: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 formerlythe smallest known pattern with superlinear growth, but has since been superseded by the related
metacatacryst. The catacryst consists of three arks plus a glider-producing switch engine. Itproduces a block-laying switch engine every 47616 generations. Each block-laying switch enginehas only a finite life, but the length of this life increases linearly with each new switch engine, sothat the pattern overall grows quadratically, as an unusual type of MMS breeder.
:catalyst An object that participates in a reaction but emerges from it unharmed. The term is mostlyapplied to still lifes, but can also be used of oscillators, spaceships, etc. The still lifes and oscillatorswhich form a conduit are examples of catalysts.
:caterer (p3) Found by Dean Hickerson, August 1989. Compare with jam. In terms of its minimumpopulation of 12 this is the smallest p3 oscillator. See also double caterer and triple caterer.
..O.....
O...OOOO
O...O...
O.......
...O....
.OO.....
More generally, any oscillator which serves up a bit in the same manner may be referred to as a
caterer.
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:Caterpillar A spaceship that works by laying tracks at its front end. The only example constructedto date is a p270 17c/45 spaceship built by Gabriel Nivasch in December 2004, based on work byhimself, Jason Summers and David Bell. This Caterpillar has a population of about 12 million ineach generation and was put together by a computer program that Nivasch wrote. It is by far thelargest and most complex Life object ever constructed.
The 17c/45 Caterpillar is based on the following reaction between a pi-heptomino and a blinker:
...............O
O.............OO
O............OO.
O.............OO
...............O
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 inSeptember 2002 that David Bell suggested that it could be used to build a 17c/45 spaceship, basedon a reaction he had found in which pis crawling along two rows of blinkers interact to emit a gliderevery 45 generations. Similar glider-emitting interactions were later found by Gabriel Nivasch andJason Summers. The basic idea of the spaceship design is that streams of gliders created in this waycan be used to construct fleets of standard spaceships 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 topleft 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.
.OO.....................
...O....................
...O.OO.................
OOO....O................
.......O................
.....OOO................
........................
........................
........................
........................
........................
........................
.....................OOO
.....................O..
......................O.
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:Catherine wheel = pinwheel
:cauldron (p8) Found in 1971 independently by Don Woods and Robert Wainwright. Compare withHertz oscillator.
.....O.....
....O.O....
.....O.....
...........
...OOOOO...
O.O.....O.O
OO.O...O.OO
...O...O...
...O...O...
....OOO....
...........
....OO.O...
....O.OO...
: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 cellularautomaton consists of a number of things. First there is a positive integer n which is the dimensionof the cellular automaton. Then there is a finite set of states S, with at least two members. A state forthe whole cellular automaton is obtained by assigning an element of S to each point of the n-dimensional lattice Zn (where Z is the set of all integers). The points of Zn are usually called cells.The cellular automaton also has the concept of a neighbourhood. The neighbourhood N of the originis some finite (nonempty) subset of Zn. The neighbourhood of any other cell is obtained in theobvious way by translating that of the origin. Finally there is a transition rule, which is a function
from SN to S (that is to say, for each possible state of the neighbourhood the transition rule specifiessome cell state). The state of the cellular automaton evolves in discrete time, with the state of eachcell at time t+1 being determined by the state of its neighbourhood at time t, in accordance with thetransition rule.
There are some variations on the above definition. It is common to require that there be a quiescentstate, that is, a state such that if the whole universe is in that state at generation 0 then it will remainso in generation 1. (In Life the OFF state is quiescent, but the ON state is not.) Other variationsallow spaces other than Zn, neighbourhoods that vary over space and/or time, probabilistic or othernon-deterministic transition rules, etc.
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It is common for the neighbourhood of a cell to be the 3...3 (hyper)cube centred on that cell.(This includes those cases where the neighbourhood might more naturally be thought of as a propersubset 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).OO................................................OO
.O................................................O.
.O.O.....................OO.....................O.O.
..OO........O............OO............OO.......OO..
...........OO..........................O.O..........
..........OO.............................O..........
...........OO..OO......................OOO..........
....................................................
....................................................
....................................................
...........OO..OO......................OOO..........
..........OO.............................O..........
...........OO..........................O.O..........
..OO........O............OO............OO.......OO..
.O.O.....................OO.....................O.O.
.O................................................O.
OO................................................OO
:century (stabilizes at time 103) This is a common pattern which evolves into three blocks and ablinker. In June 1996 Dave Buckingham built a neat p246 glider gun using a century as the engine.See also bookend and diuresis.
..OO
OOO.
.O..
:chemist (p5)
.......O.......
.......OOO.....
..........O....
.....OOO..O..OO
....O.O.O.O.O.O
....O...O.O.O..
.OO.O.....O.OO.
..O.O.O...O....
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O.O.O.O.O.O....
OO..O..OOO.....
....O..........
.....OOO.......
.......O.......
:C-heptomino Name given by Conway to the following heptomino, a less common variant of theB-heptomino.
.OOO
OOO.
.O..
:Cheshire cat A block predecessor by C. R. Tompkins that unaccountably appeared both in
Scientific American and in Winning Ways. See also grin..O..O.
.OOOO.
O....O
O.OO.O
O....O
.OOOO.
:chicken wire A type of stable agar of density 1/2. The simplest version is formed from the tile:
OO..
..OO
But the "wires" can have length greater than two and need not all be the same. For example:
OO...OOOO.....
..OOO....OOOOO
:cigar = mango
:cis-beacon on anvil (p2)
...OO.
....O.
.O....
.OO...
......
.OOOO.
O....O
.OOO.O
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...O.OO
:cis-beacon on table (p2)
..OO
...O
O...
OO..
....
OOOO
O..O
:cis-boat with tail (p1)
.O...
O.O..
OO.O.
...O.
...OO
:cis fuse with two tails (p1) See also pulsar quadrant.
...O..
.OOO..
O...OO
.O..O.
..O.O.
...O..
:cis-mirrored R-bee (p1)
.OO.OO.
O.O.O.O
O.O.O.O
.O...O.
:cis snake = canoe
:clean Opposite of dirty. A reaction which produces a small number of different products which aredesired or which are easily deleted is said to be clean. For example, a puffer which produces justone object per period is clean. Clean reactions are useful because they can be used as building
blocks in larger constructions.
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When a fuse is said to be clean, or to burn cleanly, this usually means that no debris at all is leftbehind.
: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...O.
O.O.
.O.O
.O..
:clock II (p4) Compare with pinwheel.
......OO....
......OO....
............
....OOOO....
OO.O....O...
OO.O..O.O...
...O..O.O.OO
...O.O..O.OO
....OOOO....
............
....OO......
....OO......
:cloud of smoke = smoke
:cloverleafThis name was given by Robert Wainwright to his p2 oscillator washing machine. ButAchim 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 doesnot 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.
....OOOOOO
..OO.....O
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OO.O.....O
....O...O.
......O...
......OO..
.....OOOO.
.....OO.OO
.......OO.
:Coe's p8 (p8) Found by Tim Coe in August 1997.
OO..........
OO..OO......
.....OO.....
....O..O....
.......O..OO
.....O.O..OO
:colorized Life A cellular automaton which is the same as Life except for the use of a number ofdifferent ON states ("colours"). All ON states behave the same for the purpose of applying the Liferule, but additional rules are used to specify the colour of the resulting ON cells. Examples areImmigration 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 areflector. 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 isthen considered to be white, and all other cells to be black or white in a checkerboard pattern. (Sothe cell with coordinates (m,n) is white if m+n is even, and black otherwise.) Then the colour of aglider is the colour of its leading cell when it is in a phase which can be rotated to look like this:
OOO
..O
.O.
A reflector which does not change the colour of gliders obviously cannot be used to move a glideronto a path of different colour than it started on. But a 90-degree reflector which does change thecolour of gliders is similarly limited, as the colour of the resulting glider will depend only on thedirection of the glider, no matter how many reflectors are used. For maximum flexibility, therefore,
both types of reflector are required.
:complementary blinker = fore and back
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:compression = repeat time
:conduit Any arrangement of still lifes and/or oscillators which move an active object to anotherlocation, perhaps also transforming it into a different active object at the same time, but withoutleaving 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 thefollowing remarkable one (Dave Buckingham, July 1996) in which a B-heptomino is transformedinto a Herschel in 59 generations.
.........OO.O
O.OO......OOO
OO.O.......O.
.............
.........OO..
.........OO..
:confused eaters (p4) Found by Dave Buckingham before 1973.
O..........
OOO........
...O.......
..O........
..O..O.....
.....O.....
...O.O.....
...OO..OO..
.......O.O.
.........O.
.........OO
:converter A conduit in which the input object is not of the same type as the output object. Thisterm 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 byDave Buckingham in a larger form (using a figure-8 instead of the boat). The improvement shownhere is by Bill Gosper (August 1996). Dieter Leithner has since found (much larger) oscillators of
periods 44, 46 and 60 to replace the Kok's galaxy.
.O.O..O........
.OOO.O.OO......
O......O.....O.
.O.....OO...O.O
.............OO
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OO.....O.......
.O......O......
OO.O.OOO.......
..O..O.O.......
............OOO
............O.O
............O.O
:convoy A collection of spaceships all moving in the same direction at the same speed.
:Corder- Prefix used for things involving switch engines, after Charles Corderman.
:Corder engine = switch engine
:Cordergun A gun firing Corderships. The first was built by Jason Summers in July 1999, using aglider synthesis by Stephen Silver.
:Cordership Any spaceship based on switch engines. These necessarily move at a speed of c/12diagonally with a period of 96 (or a multiple thereof). The first was found by Dean Hickerson inApril 1991. Corderships are the slowest spaceships so far constructed, although arbitrarily slowspaceships are known to exist (see universal constructor). Hickerson's original Cordership used 13switch 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.
................................OO.O...........................
...............................OOO.O......O.O..................
..............................O....O.O....O....................
...............................OO......O.O...O.................
................................O...O..O..OO...................
...................................O.OO...O....................
..................................O.O................OO........
..................................O.O................OO........
...............................................................
...............................................................
...............................................................
...............................................................
...............................................................
...............................................................
.............................................................OO
....................................................OO.......OO
.......................................O.........O.OOOO........
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..................................O...OOOOO.....OO.O...OO......
.................................O.O.......OO....O..OO.OO......
.................................O.......O.OO.....OOOOOO.......
..................................O........OO......O...........
...................................O...OOOO....................
........................................OOO....................
........................O.O.........OO.........................
........................O.O.O......O.O.........................
.......................O..OO.O....OO...........................
........................OO...O.O.OO.O..........................
........................OO...OO.OOOOO..........................
............................O.OO...OO..........................
...........................O.O.................................
..OO.O.........................................................
.OOO.O......O.O................................................
O....O.O....O..................................................
.OO......O.O...O...............................................
..O...O..O..OO...........O.....................................
.....O.OO...O...........OOO....................................
....O.O.................O..O...................................
....O.O................O....O..................................
........................O......................................
...............................................................
........................O..O...................................
.........................O.O...................................
...............................................................
.....................O.........................................
....................OOO........................................
...................OO.OO.......................................
.........O........OO.O.....O...................................
....O...OOOOO....OO......OO....................................
...O.O.......OO..OO.......OO...................................
...O.......O.OO................................................
....O........OO................................................
.....O...OOOO..................................................
..........OOO..................................................
...............................................................
...............................................................
...............................................................
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...........OO..................................................
...........OO..................................................
:cousins (p3) This contains two copies of the stillater rotor.
.....O.OO....
...OOO.O.O...
O.O......O...
OO.OO.OO.O.OO
...O.O....O.O
...O.O.OOO...
....OO.O.....
:cover The following induction coil. See scrubber for an example of its use.
....O
..OOO
.O...
.O...
OO...
:covered table = cap
:cow (c p8 fuse)
OO.......OO..OO..OO..OO..OO..OO..OO..OO..OO..OO..OO..OO.....
OO....O.OOO..OO..OO..OO..OO..OO..OO..OO..OO..OO..OO..OO...OO
....OO.O.................................................O.O
....OO...OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO..
....OO.O..................................................O.
OO....O.OOO..OO..OO..OO..OO..OO..OO..OO..OO..OO..OO..OO..OO.
OO.......OO..OO..OO..OO..OO..OO..OO..OO..OO..OO..OO..OO.....
:CP pulsar = pulsar
:crane (c/4 diagonally, p4) The following spaceship found by Nicolay Beluchenko in September2005, a minor modification of a tubeater found earlier by Hartmut Holzwart. The wing is of thesame form as in the swan and Canada goose.
.OO.................
OO..................
..O.................
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....OO...O..........
....OO..O.O.........
.......OO.O.........
.......OO...........
.......OO...........
.................OO.
.........O....OO.O..
.........OOO..OO....
.........OOO..OO....
..........OO........
....................
............O.......
...........OO.......
...........O........
............O.......
....................
.............OO.....
..............O.OO..
..................O.
...............OO...
...............OO...
.................O..
..................OO
:cross (p3) Found by Robert Wainwright in October 1989.
..OOOO..
..O..O..
OOO..OOO
O......O
O......O
OOO..OOO
..O..O..
..OOOO..
In February 1993, Hartmut Holzwart noticed that this is merely the smallest of an infinite family ofp3 oscillators. The next smallest member is shown below.
..OOOO.OOOO..
..O..O.O..O..
OOO..OOO..OOO
O...........O
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O...........O
OOO.......OOO
..O.......O..
OOO.......OOO
O...........O
O...........O
OOO..OOO..OOO
..O..O.O..O..
..OOOO.OOOO..
:crowd (p3) Found by Dave Buckingham in January 1973.
...........O..
.........OOO..
.....OO.O.....
.....O...O....
.......OO.O...
...OOOO...O...
O.O.....O.O.OO
OO.O.O.....O.O
...O...OOOO...
...O.OO.......
....O...O.....
.....O.OO.....
..OOO.........
..O...........
:crown The p12 part of the following p12 oscillator, where it is hassled by caterer, a jam and a HWemulator. This oscillator was found by Noam Elkies in January 1995.
..........O...........
..........O......O....
...O....O...O...OO....
...OO....OOO..........
.........OOO..OOO..O.O
.O..OOO.........O.OOOO
O.O.O...............OO
O..O..................
.OO........OO.........
......OO.O....O.OO....
......O..........O....
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:dart (c/3 orthogonally, p3) Found by David Bell, May 1992.
.......O.......
......O.O......
.....O...O.....
......OOO......
...............
....OO...OO....
..O...O.O...O..
.OO...O.O...OO.
O.....O.O.....O
.O.OO.O.O.OO.O.
:dead spark coil (p1) Compare spark coil.
OO...OO
O.O.O.O
..O.O..
O.O.O.O
OO...OO
:de Bruijn diagram = de Bruijn graph
:de Bruijn graph As applied to Life, a de Bruijn graph is a graph showing which pieces can belinked 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 lifes, then we could consider 23 rectangular pieces and thede Bruijn graph would show which pairs of these can be overlapped to form 33 squares in whichthe 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 unitcell simulates two Life cells, in such a way that a Life universe filled with Deep Cells simulates twoindependent Life universes running in parallel.
In fact, a Life universe filled with Deep Cells can simulate infinitely many Life universes, asfollows. Let P1, P2, P3, ... be a sequence of Life patterns. Set the Deep Cells to run a simulation ofP1 in parallel with a simulation of a universe filled with Deep Cells, with these simulated DeepCells running a simulation of P2 in parallel with another simulation of a universe filled with DeepCells, with these doubly simulated Deep Cells simulating P3 in parallel with yet another universe of
Deep Cells, and so on.
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:diehard Any pattern that vanishes, but only after a long time. The following example vanishes in130 generations, which is probably the limit for patterns of 7 or fewer cells. Note that there is nolimit for higher numbers of cells - e.g., for 8 cells we could have a glider heading towards anarbitrarily distant blinker.
......O.
OO......
.O...OOO
:dinner table (p12) Found by Robert Wainwright in 1972.
.O...........
.OOO.......OO
....O......O.
...OO....O.O.
.........OO..
.............
.....OOO.....
.....OOO.....
..OO.........
.O.O....OO...
.O......O....
OO.......OOO.
...........O.
:dirty Opposite of clean. A reaction which produces a large amount of complicated junk which isdifficult to control or use is said to be dirty. Many basic puffer engines are dirty and need to betamed by accompanying spaceships in order to produce clean output.
:diuresis (p90) Found by David Eppstein in October 1998. His original stabilization usedpentadecathlons. The stabilization with complicated still lifes shown here (in two slightly differentforms) was found by Dean Hickerson the following day. The name is due to Bill Gosper (seekidney).
.....OO................OO....
......O................O.....
......O.O............O.O.....
.......OO............OO......
.............................
....OO..................OO...
....O.O..........OO....O.O...
.....O..........O.O.....O....
..O.............OO.........O.
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..OOOOOO........O.....OOOOOO.
.......O..............O......
....OO..................OO...
....O....................O...
.....O..................O....
..OOO..O..............O..OOO.
..O..OOO........O.....OOO...O
...O............OO.......OOO.
....OO..........O.O.....O....
......O..........OO....O..OO.
....OO..................OO.O.
.O..O....................O...
O.O.O..OO............OO..O...
.O..O.O.O............O.O.OO..
....O.O................O..O..
.....OO................OO....
:dockThe following induction coil.
.OOOO.
O....O
OO..OO
:domino The 2-cell polyomino. A number of objects, such as the HWSS and pentadecathlon,produce domino sparks.
:do-see-do The following reaction, found by David Bell in 1996, in which two gliders appear tocircle around each other as they are reflected 90 degrees by a twin bees shuttle. Four copies of thereaction can be used to create a p92 glider loop which repeats the do-see-do reaction forever.
.....................................................O.O
.....................................................OO.
......................................................O.
........................................................
........................................................
........................................................
........................................................
........................................................
........................................................
........................................................
........................................................
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........................................................
........................................................
........................................................
........................................................
........................................................
........................................................
........................................................
........................................................
................................................OO......
................................................O.......
..............................................O.O.......
..............................................OO........
..............................O.O.......................
..............................OO........................
...............................O........................
........................................................
.......................OOO..............................
OO........OOO........OO.O.OO............................
OO........O...O.....O.....OO............................
..........O....O.....OO.O.OO............................
...........O...O.......OOO..............................
........................................................
...........O...O........................................
..........O....O........................................
OO........O...O............OO...........................
OO........OOO..............OO...........................
:double-barrelled Of a gun, emitting two streams of spaceships (or rakes). See B-52 bomber for anexample.
: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 apair of blocks eats an R-pentomino and a LWSS. (The LWSS version was known at least as early1994, when Paul Callahan saw it form spontaneously as a result of firing a LWSS stream at somerandom junk.)
.OOOO.....OO....
O...O......OO.OO
....O......O..OO
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O..O............
................
.............OO.
.............OO.
:double caterer (p3) Found by Dean Hickerson, October 1989. Compare caterer and triple caterer.
.....OO...O........
....O..O..OOO......
....OO.O.....O.....
......O.OOOO.O.....
..OOO.O.O...O.OO...
.O..O..O...O..O.O..
O.O..O...O.OO....O.
.O..........OO.OOO.
..OO.OO.OO...O.....
...O...O.....O.OOO.
...O...O......OO..O
.................OO
:double ewe (p3) Found by Robert Wainwright before September 1971.
......OO............
.......O............
......O.............
......OO............
.........OO.........
......OOO.O.........
O.OO.O..............
OO.O.O..............
.....O...O..........
....O...OO....OO....
....OO....OO...O....
..........O...O.....
..............O.O.OO
..............O.OO.O
.........O.OOO......
.........OO.........
............OO......
.............O......
............O.......
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............OO......
:double wing = moose antlers
:dove The following induction coil.
.OO..
O..O.
.O..O
..OOO
:down boat with tail = cis-boat with tail
:dragon (c/6 orthogonally, p6) This spaceship, discovered by Paul Tooke in April 2000, was thefirst known c/6 spaceship. All other known orthogonal c/6 spaceships are flotillas involving at leasttwo dragons.
.............O..OO......O..OOO
.....O...OOOO.OOOOOO....O..OOO
.OOOOO....O....O....OOO.......
O......OO.O......OO.OOO..O.OOO
.OOOOO.OOO........OOOO...O.OOO
.....O..O..............O......
........OO..........OO.OO.....
........OO..........OO.OO.....
.....O..O..............O......
.OOOOO.OOO........OOOO...O.OOO
O......OO.O......OO.OOO..O.OOO
.OOOOO....O....O....OOO.......
.....O...OOOO.OOOOOO....O..OOO
.............O..OO......O..OOO
:drain trap = paperclip
:drifter A perturbation moving within a stable pattern. Dean Hickerson has written a program tosearch for drifters, with the hope of finding one which could be moved around a track. Becausedrifters can be very small, they could be packed more tightly than Herschels, and so allow thecreation of oscillators 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 changethe 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 eaters with novel properties, such
as that used in diuresis.
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:dual 1-2-3-4 = Achim's p4
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.......OO.OOOO
.........O....
.........O.O..
..........OO..
:eater/block frob (p4) Found by Dave Buckingham in 1976 or earlier.
.OO.......
..O.......
..O.O.....
...O.O....
.....OO.OO
........OO
..OO......
...O......
OOO.......
O.........
: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.
.......O
.....OOO
....O...
.....O..
..O..O..
.O.OO...
.O......
OO......
:eaters + = French kiss
:eaters plus = French kiss
:ecologist (c/2 orthogonally, p20) This consists of the classic puffer train with a LWSS added to
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suppress the debris. See also space rake.
OOOO.....OO........
O...O...OO.OO......
O........OOOO......
.O..O.....OO.......
...................
.....O.........OO..
...OOO........OOOOO
..O...O.....O....OO
..O....OOOOO.....OO
..OO.O.OOOO....OO..
....O...OO.OOO.....
.....O.O...........
...................
...................
OOOO...............
O...O..............
O..................
.O..O..............
:edge-repair spaceship A spaceship which has an edge that possesses no spark and yet is able toperturb 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 spaceships:
..................................O.....
........O.......................OOO.OOO.
.......OOOO....................OO......O
..O...O...OO.OO...........O...O..O...OO.
.OOOO.....O..OO..........OOOO...........
O...O.......O..O........O...O...........
.O.O..O..................O.O..O.........
.....O.......................O..........
These were found by David Bell in 1992, but the usefulness of the edge-repair property wasn'trecognised until July 1997. The following diagram (showing an edge-repair spaceship deleting aHerschel) demonstrates the self-repairing action.
................O.......
O..............OOOO.....
O.O.......O...O...OO.OO.
OOO......OOOO.....O..OO.
..O.....O...O.......O..O
.........O.O..O.........
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.............O..........
In October 2000, David Bell found that a T-tetromino component of a c/4 spaceship can also beself-repairing. Stephen Silver noticed that it could be used to delete beehives and, in November2000, found the smallest known c/4 spaceship with this edge-repair component - in fact, two copiesof the component:
.OO..........................
O..O.........................
.OO..........................
.............................
.......O.O...................
.......O.....................
.......O.O..O..O.............
..........O..................
...........O.OO.O............
............OOO.O............
...........O....O..O.OO......
........O...OO...O.OOOO......
........OO..O..O.OO....O....O
........O........OO....O..OOO
.............OO...OO...O..OO.
.OO..........................
O..O.........................
.OO..........................
:edge shooter A gun which fires its gliders (or whatever) right at the edge of the pattern, so that itcan 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.
OO............OO..O....OO..OO.............
OO............O.OO......OO.OO.............
...............O......O.O.................
...............OOO....OO..................
..........................................
...............OOO....OO..................
...............O......O.O.................
OO............O.OO......OO................
OO............OO..O....OO.................
..........................................
..........................................
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..........................................
..........................................
..........................................
..........................................
...............................OOO...OOO..
..............................O...O.O...O.
.............................O...OO.OO...O
.............................O.OO.....OO.O
...............................O.......O..
..........................................
..........................................
..........................................
..........................................
..........................................
..........................................
..........................................
..........................................
..........................................
..........................................
...............................OO.....OO..
...............................OO.....OO..
:edge sparkA spark at the side of a spaceship that can be used to perturb things as the spaceshippasses by.
:edge sparker A spaceship that produces one or more edge sparks.
:egg = non-spark
:E-heptomino Name given by Conway to the following heptomino..OOO
OO..
.OO.
:elbow ladder Scot Ellison's name for the type of pattern he created in which one or more glidersshuttle back and forth (using the kickback reaction) deleting the output gliders from a pair of slideguns.
:electric fence (p5) A stabilization of ants. Dean Hickerson, February 1993.
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..........O..................................................
.........O.O........................OO.......................
..O....OOO.O.....O...................O...O..O......O.....OO..
.O.O..O....OO...O.O..................O.OOO..OOO...O.O....O...
.O.O..O.OO.......O....................O...OO...O.O..O......O.
OO.OO.O.O.OOOOO.....O..................OO...O..O.O.OO.OO..OO.
.O.O..O...O..O..O.......OO...OO...OO....OO.OO..O.O..O.O.O....
.O..OO....OO......OOO.OO...OO...OO...OOO.....OOOO.OOO.O...OO.
..O..OOO..O..O.OOOO...OO...OO...OO...OOO.OO..O....O.O....O..O
...OO...O.O..O.....OO...OO...OO...OO......O............O...OO
.....OO.O.OO.O.OO..O......................O........OO.O......
.....O.OO.O..O.OO....O.................OO.O.O................
...........OO.......OO..................O..OO................
......................................O.O....................
......................................OO.....................
:elevener (p1)
OO....
O.O...
..O...
..OOO.
.....O
....OO
:Elkies' p5 (p5) Found by Noam Elkies in 1997.
.O.......
O..OOO...
..O......
...O.O..O
..OO.OOOO
....O....
....O.O..
.....OO..
:emu Dave Buckingham's term for a Herschel loop that does not emit gliders (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 sparks similar to those produced by LWSS,
MWSS and HWSS. See LW emulator, MW emulator and HW emulator. Larger emulators are also
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possible, but they require stabilizing objects to suppress their non-sparks and so are of little use. Theemulators were discovered by Robert Wainwright in June 1980.
:engine The active portion of an object (usually a puffer or gun) which is considered to actuallyproduce 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, blinkerpuffer, frothing puffer and line puffer.
:en retard (p3) Found by Dave Buckingham, August 1972.
.....O.....
....O.O....
OO.O.O.O.OO
.O.O...O.O.
O..O.O.O..O
.OO.....OO.
...OO.OO...
...O.O.O...
....O.O....
..O.O.O.O..
..OO...OO..
:Enterprise (c/4 diagonally, p4) Found by Dean Hickerson, March 1993.
.......OOO...........
.....O.OO............
....OOOO.............
...OO.....O..........
..OOO..O.O.O.........
.OO...O.O..O.........
.O.O.OOOOO...........
OO.O.O...O...........
O........OO..........
.OO..O...O.O.........
....OO..O.OO......O..
...........OO.....OOO
............O..OOO..O
............O..O..OO.
.............O.OO....
............OO.......
............OO.......
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...........O.........
............O.O......
...........O..O......
.............O.......
:Eureka (p30) A pre-pulsar shuttle found by Dave Buckingham in August 1980. A variant isobtained by shifting the top half two spaces to either side.
.O..............O.
O.O....O.......O.O
.O...OO.OO......O.
.......O..........
..................
..................
..................
.......O..........
.O...OO.OO......O.
O.O....O.......O.O
.O..............O.
:evolutionary factor For an unstable pattern, the time to stabilization divided by the initialpopulation. For example, the R-pentomino has an evolutionary factor of 220.6, while bunnies has anevolutionary factor of 1925.777... The term is no longer in use.
:exposure = underpopulation
:extensible A pattern is said to be extensible if arbitrarily large patterns of the same type can bemade 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.
....OO......
...O.OOO....
...O....O...
OO.O...OO...
OO.O.....OO.
....OOOOO..O
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..........OO
......O.....
.....O.O....
......O.....
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:factory Another word for gun, but not used in the case of glider guns. The term is also used for apattern that repeatedly manufactures objects other than spaceships or rakes. In this case the newobjects do not move out of the way, and therefore must be used up in some way before the next oneis made. The following shows an example of a p144 gun which consists of a p144 block factorywhose output is converted into gliders by a p72 oscillator. (This gun is David Bell's improvement ofthe 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.).......................OO........................OO
.......................OO........................OO
.........................................OO........
........................................O..O.......
.........................................OO........
...................................................
....................................OOO............
....................................O.O............
.........OO.........................OOO............
.........OO.........................OO.............
........O..O.......................OOO.............
........O..O.OO....................O.O.............
........O....OO....................OOO.............
..........OO.OO....................................
...............................OO..................
.....................OO.......O..O.................
.....................OO........OO..................
.................................................OO
.................................................OO
...................................................
....OO..................O..........................
OO....OOOO..........OO..OO.OOO.....................
OO..OO.OOO..........OO....OOOO.....................
....O...................OO.........................
:familiar fours Common patterns of four identical objects. The five commonest are traffic light (4blinkers), 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 gliders or Herschels; glider duplicators 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
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allow the LWSS to advance 11 spaces in the course of the next 6 generations. A neat illusion. Seealso star gate. (Leithner named the Fast Forward Force Field in honour of his favourite sciencefiction writer, the physicist Robert L. Forward.)
.......O......O..
........O......OO
..OO..OOO.....OO.OO.OO............
OOOO.........O...
.OO.........OO...
............O.O..
:father = parent
: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 exhibitsinfinite growth if and only if there are no Fermat primes greater than 65537. The question ofwhether
