This lexicon was compiled by Stephen Silver - see below for additional credits. I can be contacted at sas@cafenet.co.uk or sasilver@hotmail.com.
Other sources include volume 2 of "Winning Ways" (by Elwyn Berlekamp, John Conway and Richard Guy), various articles by Martin Gardner, "The Recursive Universe" by William Poundstone, issue 1 of LifeLine (edited by Robert Wainwright), " Spaceships in Conway's Life" by David Bell, "My Experience with B-heptominos in Oscillators" by Dave Buckingham, pattern collections by Alan Hensel and David Bell (and especially Dean Hickerson's file stamp.l in the latter collection), and the web sites of Mark Niemiec, Paul Callahan, Achim Flammenkamp and Heinrich Koenig.
Dean Hickerson, David Bell and especially Alan Hensel provided some useful comments on earlier releases of this lexicon.
The format, errors, use of British English and anything else you might want to complain about are by Stephen Silver.
Digits lexicographically precede letters. Any term that contains no alphanumeric characters at all will be found at the very beginning of the lexicon.
The main thing to note about the format of the HTML version is that all keywords are preceded by a colon. For example, entering :foo in the dialogue box of your browser's Find command will take you straight to the definition of the first word beginning with "foo" (or at least it would if there were any). This is the recommended way of finding a particular definition when there is no link to click on.
The diagrams in this lexicon are in a very standard format. You should be able to simply copy a pattern, paste it into a new file and run it in your favourite Life program. This works at least with Alan Hensel's DOS program. (Actually, it didn't work too well when I tried it with Microsoft Internet Explorer. This doesn't allow the last cell of the diagram to be copied without copying the whole of the rest of the file. I kid thee not. This happens with version 3.0a.1563. Of course, they might have got it right at the 1564th attempt.) I have restricted myself to diagrams of size 64x64 or less.
Most definitions that have a diagram have also some data in brackets after the keyword. Oscillators are maked as pn (where n is a number), meaning that the period is n (p1 indicates a still life). Wicks are marked in the same way but with the word "wick" added. For spaceships the speed (as a fraction of c, the speed of light), the direction and the period are given. Fuses are marked with speed and period and have the word "fuse" added. Wicks and fuses are infinite in extent and so have necessarily been truncated, with the ends stabilized wherever practical.
If you spot any errors, then please tell me.
There are certainly numerous omissions, especially in my failure to assign a discoverer to many interesting patterns. Dates of discovery are omitted even more frequently. Any information would be welcome.
:][ = table on table
:101 (p5)
....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....
.....O..... ....O.O.... ...O.O.O... ...O...O... OO.O.O.O.OO O.O.....O.O ...OOOOO... ........... .....O..... ....O.O.... .....O.....
:14-ner = fourteener
:2 eaters = two eaters
:4-8-12 diamond The following pure glider generator.
....OOOO.... ............ ..OOOOOOOO.. ............ OOOOOOOOOOOO ............ ..OOOOOOOO.. ............ ....OOOO....
:Achim's p144 (p144) This was found in an infinite form by Achim Flammenkamp in 1994. The stabilizing blocks in the finite form shown here were found by David Bell. See the gun shown under 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.
.......OO.... .......O.O... ..O....O.OO.. .OO.....O.... O..O......... OOO.......... ............. ..........OOO .........O..O ....O.....OO. ..OO.O....O.. ...O.O....... ....OO.......
:Achim's p4 = cloverleaf
:Achim's p5 = pseudo-barberpole
:acorn (stabilizes at time 5206) A methuselah found by Charles Corderman.
.O..... ...O... OO..OOO
:A for All (p6)
....OO.... ...O..O... ...OOOO... .O.O..O.O. O........O O........O .O.O..O.O. ...OOOO... ...O..O... ....OO....
:agar Any periodic tiling of the plane that results in an infinite still life or oscillator. The simplest agar is the one extended by the known spacefillers. The following diagram shows another simple stable agar. (Some cells have been removed from the outer edge of this diagram in order to make the finite form stable.)
.OO....OO....OO....OO....OO....OO. O..O..O..O..O..O..O..O..O..O..O..O O..O..O..O..O..O..O..O..O..O..O..O .OO.OO.OO.OO.OO.OO.OO.OO.OO.OO.OO. ...O..O..O..O..O..O..O..O..O..O... ...O..O..O..O..O..O..O..O..O..O... .OO.OO.OO.OO.OO.OO.OO.OO.OO.OO.OO. O..O..O..O..O..O..O..O..O..O..O..O O..O..O..O..O..O..O..O..O..O..O..O .OO.OO.OO.OO.OO.OO.OO.OO.OO.OO.OO. ...O..O..O..O..O..O..O..O..O..O... ...O..O..O..O..O..O..O..O..O..O... ....OO....OO....OO....OO....OO....
OO.. O..O ..OO
:airforce (p7) Found by Dave Buckingham.
.......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) in which a honey farm predecessor, catalysed by an eater and a block, reappears at another location 47 generations later, having produced a glider and a traffic light. This is the basis of a neat (but pseudo) p94 glider gun found by Paul Callahan.
.....O.... ....O.O... ...O...O.. ...O...O.. ...O...O.. ....O.O... .....O.... .......... ..OO...... ...O...... OOO.....OO O.......OO
:Al Jolson (p15) Two blocks hassled by two pentadecathlons. A p9 version using snackers instead of pentadecathlons is also possible.
.OO......OO.. O..O....O..O. O..O....O..O. O..O....O..O. .OO......OO.. ............. ............. .......O..... .....O..O.OO. ......OO..OO. ............. ............. ......OOOO... .....OOOOOO.. ....OOOOOOOO. ...OO......OO ....OOOOOOOO. .....OOOOOO.. ......OOOO...
:antlers = moose antlers
:ants (p5 wick) The standard form is shown below. It is also possible for any ant to be displaced by one cell relative to either or both of its neighbouring cells. Dean Hickerson found fenceposts for both ends of this wick in 1992.
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 OO...OO...OO...OO...OO...OO...OO...OO...OO..
:anvil The following induction coil.
.OOOO. O....O .OOO.O ...O.OO
:arm A long extension hanging off from the main body of a spaceship or puffer at right angles to the direction of travel. A lot of known spaceships, particularly c/3 ones, have multiple arms. This is an artefact of the search methods used to find such spaceships, rather than an indication of what a "typical" spaceship might look like.
:ash The (stable or oscillating) debris left by a random reaction.
:aVerage (p5) Found by Dave Buckingham.
...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........
:B = B-heptomino
:babbling brook Any oscillator whose rotor consists of a string of cells each of which is adjacent to exactly two other rotor cells, except for the endpoints which are adjacent to only one other rotor cell. Compare muttering moat. Examples include the beacon and the light bulb. The following is a less trivial p4 example.
....OO..... ...O.O..... ...O....... OO.OO...... OO.O.O...OO ...O.O....O ...O..OOOO. ..OO....... ......OO... ......OO...
:backrake Another term for a backward rake.
:baker (c p4 fuse) A fuse by Keith McClelland.
..............OO .............O.O ............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.
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....
:barberpole Any p2 oscillator in the infinite series bipole, tripole, quadpole, pentapole, hexapole, heptapole ... (It wasn't my idea to suddenly change from Latin to Greek.) The term is also used to describe other extensible sections of oscillators or spaceships, especially those (usually of period 2) in which all generations look alike except for a translation and/or rotation/reflection.
:barberpole intersection = quad
:barber's pole = barberpole
:barge (p1)
.O.. O.O. .O.O ..O.
:beacon (p2) The third most common oscillator.
OO.. O... ...O ..OO
..............OO .............O.O ............O... ...........O.... ..........O..... .........O...... ........O....... .......O........ ......O......... .....O.......... ....O........... ...O............ OOO............. ..O............. ..O.............
:beehive (p1) The second most common still life.
.OO. O..O .OO.
...OO. ..O..O ...OO. ...... .OOOO. O....O OO..OO
:beehive on big table = beehive and dock
:beehive pusher = hive-nudger
:beehive with tail (p1)
.OO... O..O.. .OO.O. ....O. ....OO
:belly spark The spark of a MWSS or HWSS other than the tail spark.
:B-heptomino (stabilizes at time 148) This is a very common pattern. It often arises with the cell at top left shifted one space to the left, which does not affect the subsequent evolution. B-heptominoes have acquired particular importance of late 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) This is the smallest pseudo still life.
OO.OO OO.OO
:bi-boat = boat-tie
:biclock The following pure glider generator.
..O.... OO..... ..OO... .O...O. ...OO.. .....OO ....O..
:big beacon = figure-8
:big fish = HWSS
....OO. ...O..O ...O.OO OO.O... O..O... .OO....
:billiard table configuration Any oscillator in which the rotor is enclosed within the stator. Examples include airforce, cauldron, clock II, Hertz oscillator, negentropy, pinwheel, pressure cooker and scrubber.
:bi-loaf This term has been used in at least three different senses.
bi-loaf - a half bakery (p1):
.O.....
O.O....
O..O...
.OO.O..
...O.O.
...O..O
....OO.
bi-loaf - a less common still-life (p1):
..O....
.O.O...
O..O...
.OO.OO.
...O..O
...O.O.
....O..
biloaf - a 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
.OO.... O..O... O..O... .OO.OO. ...O..O ...O..O ....OO.
:bi-ship = ship-tie
:blinker (p2) The smallest and most common oscillator.
OOO
:blinker ship A growing spaceship in which the wick consists of a line of blinkers. An example based on the Schick engine is shown below. Here the front part is p12 and moves at c/2, while the back part is p26 and moves at 6c/13. Every 156 generations 13 blinkers are created and 12 are destroyed, so the wick becomes one blinker longer.
...........O..O............... ..........O................... ..........O...O............... ..OO......OOOO................ .OOOO......................... OO.OO......................... .OO.....OO.OOO................ .......O.....OO.......O....OOO ......OO.......O......O....O.O .......O.....OO.......O....OOO .OO.....OO.OOO................ OO.OO......................... .OOOO......................... ..OO......OOOO................ ..........O...O............... ..........O................... ...........O..O...............
:biting off more than they can chew = eater-bound pond
: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
...OO. ...OO. ...... .OOOO. O....O OO..OO
:block and glider (stabilizes at time 106)
OO.. O.O. ..OO
:blocker (p8) Found by Robert Wainwright. This oscillator has the property of being able to double the period of any glider or LWSS stream of period 8n+4.
......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
:blonk A block or a blinker. This term is mainly used in the context of sparse Life and was coined by Rich Schroeppel in September 1992.
:boat (p1) The only 5-pixel still life.
OO. O.O .O.
:boat-bit A binary digit represented by the presence of a boat next to a snake (or other suitable object, such as an aircraft carrier). The bit can be toggled by a glider travelling along a certain path. Its value cannot be read directly, but a correctly timed glider on a crossing path can detect whether the transition was from 1 to 0 (in which case the crossing glider is deleted) or from 0 to 1 (in which case it passes unharmed). Three gliders therefore suffice for a non-destructive read. The mechanisms involved are shown in the diagram below. Here the bit is shown in state 0. It is about to be set to 1 and then switched back to 0 again. The first crossing glider will survive, but the second will be destroyed.
......O.................. .......O................. .....OOO................. ......................... ......................... ......................... ......................... ......................... ......................... ......................... ................O........ ..............O.O........ ..........OO...OO........ ...........OO............ ..........O..........O.OO .....................OO.O ......................... ......................... ......................... ......................... ......................... .O....................... .OO...................... O.O......................
................OO ...............O.O ..............O... .............O.... ............O..... ...........O...... ..........O....... .........O........ ........O......... .......O.......... ......O........... .....O............ OOOOO............. ....O............. ....O............. ....O............. ....O.............
:boat on boat = boat-tie
:boat-ship-tie = ship on boat
:boatstretcher Any wickstretcher that stretches a boat. The first one was found by Hartmut Holzwart in 1993. The following example is by Noam Elkies and uses Tim Coe's swan. Note that in any boatstretcher the point of the boat can be removed to get a tubstretcher.
............OO.......... OOO.........O.O......... O..OOO......O.........O. .O.O................OO.O ......O....OO..O...OO..O ....O......OO..O.OO..O.. ......O.OO.O...OOOOO.... ...............OO....... .......O..OOOOOO........ ........OOOOOOO......... ..........OOO........... ........................ .............O.......... ............O.O......... .............OO.........
:boat-tie (p1) The name is a pun on "bow tie".
.O.... O.O... .OO... ...OO. ...O.O ....O.
:bookend The following induction coil. It is generation 1 of century.
..OO O..O OOO.
OO...OO O.O.O.O ..O.O.. .OO.OO.
:boss (p4)
.....O..... ....O.O.... ....O.O.... ...OO.OO... ..O.....O.. .O.O.O.O.O. .O.O...O.O. OO.O...O.OO O..O.O.O..O ..O.....O.. ...OO.OO... ....O.O.... ....O.O.... .....O.....
:bow tie = boat-tie
:brain (c/3 orthogonally, p3) Found by David Bell.
.OOO.........OOO. O.O.OO.....OO.O.O O.O.O.......O.O.O .O.OO.OO.OO.OO.O. .....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 exclude spacefillers. It is easy to see that this is the fastest possible growth rate. The term is also sometimes used to mean specifically the breeder created by Bill Gosper's group at MIT, which was the first known pattern exhibiting superlinear growth. There are four basic types of breeder, known as MMM, MMS, MSM and SMM (where S=stationary and M=moving). Typically an MMM breeder is a rake puffer, an MMS is a puffer producing puffers which produce stationary objects (still lifes and/or oscillators), an MSM breeder is a gun puffer and an SMM breeder is a rake gun. There are, however, less obvious variants of these types. The original breeder was of type MSM (a p64 puffer puffing p30 glider guns). The known breeder with the smallest initial population is Jaws.
: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 a glider, as shown below.
..O..................... O.O..................... .OO..................... ...........O............ .........O.O............ ........O.O............. .......O..O...........OO ........O.O...........OO ...OO....O.O............ ..O.O......O............ ..O..................... .OO.....................
:bun The following induction coil. By itself this is a common predecessor of the honey farm. See also cis-mirrored R-bee.
.OO. O..O .OOO
:bunnies (stabilizes at time 17332) This is a one-generation predecessor of rabbits and was found by Robert Wainwright.
O.....O. ..O...O. ..O..O.O .O.O....
:burloaf = loaf
:burloaferimeter (p7) Found by Dave Buckingham.
.....O..... ....O.O.... ...O.O.O... ...O.O.O... OO.O...O.OO OO.O....O.O ....OOOO... ........... ....OO..... ....OO.....
:bushing That part of the stator of an oscillator which is adjacent to the rotor. Compare casing.
:butterfly (p1) The following fairly common formation of two beehives.
.O............ O.O........... O.O........... .O............ .............. .............. .............. .............. .............. .............. .............. ...........OO. ..........O..O ...........OO.
:c = speed of light
:CA = cellular automaton
:caber tosser A gun of increasing period created by bouncing a glider (or some other type of spaceship) off of a receding spaceship.
:Cambridge pulsar CP 48-56-72 = pulsar (The numbers refer to the populations of the three phases.)
:candelabra (p3) By Charles Trawick. This is really three copies of a smaller oscillator. See also the note under cap.
....OO....OO.OO....OO.OO....OO.... .O..O......O.O......O.O......O..O. O.O.O......O.O..OO..O.O.O..O.O.O.O .O..O.OOOO.O.O.OOOO.O.O.O..O.O..O. ....O.O..O.O.O.O..O.O.O.O..O.O.... .....O....O...O....O...O....O.....
...OO ....O ...O. O.O.. OO...
:cap The following induction coil. It can also be easily be stabilized to form a p3 oscillator - see candelabra for a slight variation on this.
.OO. O..O OOOO
:carrier = aircraft carrier
:casing That part of the stator of an oscillator which is not adjacent to the rotor. Compare bushing.
:catalyst An object that participates in a reaction but emerges from it unharmed. The term is mostly applied to still lifes, but can also be used of oscillators, spaceships, etc. The still lifes and oscillators which form a conduit are examples of catalysts.
:caterer (p3) Found by Dean Hickerson. Compare with jam.
..O..... O...OOOO O...O... O....... ...O.... .OO.....
:Catherine wheel = pinwheel
:cauldron (p8) Found by Don Woods and Robert Wainwright. Compare with the Hertz oscillator.
.....O..... ....O.O.... .....O..... ........... ...OOOOO... O.O.....O.O OO.O...O.OO ...O...O... ...O...O... ....OOO.... ........... ....OO.O... ....O.OO...
:cavity (p2)
OO...... .O...... .O.OO... ..O..O.. .....O.. ....O... .....OOO .......O
:cell The fundamental unit of space. The term is often used to mean a live cell - the sense is usually clear from the context.
:cellular automaton A certain class of mathematical objects of which Life is an example. A cellular automaton consists of a number of things. First there is a positive integer n which is the dimension of the cellular automaton. Then there is a finite set of states S, with at least two members. A state for the whole cellular automaton is obtained by assigning an element of S to each point of the n-dimensional lattice 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 origin is some finite (nonempty) subset of Zn. The neighbourhood of any other cell is obtained in the obvious way by translating that of the origin. Finally there is a transition rule, which is a function from SN to S (that is to say, for each possible state of the neighbourhood the transition rule specifies some cell state). The state of the cellular automaton evolves in discrete time, with the state of each cell at time t+1 being determined by the state of its neighbourhood at time t, in accordance with the transition rule.
There are some variations on the above definition. It is common to require that there be a quiescent state, that is, a state such that if the whole universe is in that state at generation 0 then it will remain so in generation 1. (In Life the OFF state is quiescent, but the ON state is not.) Other variations allow spaces other than Zn, neighbourhoods that vary over space and/or time, probabilistic or other non-deterministic transistion rules, etc., etc.
It is common for the neighbourhood of a cell to be the 3x...x3 (hyper)cube centered on that cell. (This includes those cases where the neighbourhood might more naturally be thought of as a subset of this cube.) This is known as the Moore neighbourhood.
:centinal (p100) Found by Bill Gosper. This combines the mechanisms of the p46 and p54 shuttles (see twin bees shuttle and p54 shuttle).
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 a blinker. In June 1996 Dave Buckingham built a neat p246 glider gun using a century as the engine. See also bookend.
..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.... O.O.O.O.O.O.... OO..O..OOO..... ....O.......... .....OOO....... .......O.......
:C-heptomino Name given by Conway to the following 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.
:cigar = mango
:cis-beacon on anvil (p2)
...OO. ....O. .O.... .OO... ...... .OOOO. O....O .OOO.O ...O.OO
:cis-beacon on table (p2)
..OO ...O O... OO.. .... OOOO O..O
.O... O.O.. OO.O. ...O. ...OO
...O.. .OOO.. O...OO .O..O. ..O.O. ...O..
.OO.OO. O.O.O.O O.O.O.O .O...O.
:cis snake = canoe
:clock (p2) Found by Simon Norton.
..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......
:cloverleaf (p4) Found by Achim Flammenkamp. The rotor here is two copies of the rotor of the 1-2-3-4, so the cloverleaf is sometimes called the "dual 1-2-3-4". See also sombreros.
..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..
:cluster Any pattern in which each live cell is connected to every other live cell by a path that does not pass through two consecutive dead cells. This sense is due to Nick Gotts, but obviously the term has also been used more vaguely.
:Coe ship (c/2 ortogonally, p16) A puffer engine discovered by Tim Coe in October 1995.
....OOOOOO ..OO.....O OO.O.....O ....O...O. ......O... ......OO.. .....OOOO. .....OO.OO .......OO.
:Coe's p8 (p8) Found by Tim Coe in 1997.
OO.......... OO..OO...... .....OO..... ....O..O.... .......O..OO .....O.O..OO
:conduit Any arrangement of still lifes and/or oscillators which move an active object to another location, perhaps also transforming it into a different active object at the same time, but without leaving any permanent debris (except perhaps gliders, or other spaceships) and without any of the still lifes or oscillators being permanently damaged. Probably the most important conduit is the following remarkable one (Dave Buckingham, July 1996) in which a B-heptomino is transformed into a Herschel in 59 generations.
.........OO.O O.OO......OOO OO.O.......O. ............. .........OO.. .........OO..
:confused eaters (p4) Found by Dave Buckingham.
O.......... OOO........ ...O....... ..O........ ..O..O..... .....O..... ...O.O..... ...OO..OO.. .......O.O. .........O. .........OO
:Corder engine = switch engine
:Cordership Any spaceship based on switch engines. These necessarily move at a speed of c/12 diagonally with a period of 96 (or, conceivably, a multiple thereof), and the first was found by Dean Hickerson in April 1991. Corderships are by far the slowest spaceships yet constructed, although arbitrarily slow spaceships are known to exist (see universal constructor/destructor). Hickerson's original Cordership used 13 switch engines. He later reduced this to 10, and, in August 1993, to 7. Even this last, however, is too large to show here.
:cover The following induction coil. See scrubber for an example of its use.
....O ..OOO .O... .O... OO...
:covered table = cap
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
:cross (p3) Found by Robert Wainwright. This is the smallest of an infinite family of p3 oscillators.
..OOOO.. ..O..O.. OOO..OOO O......O O......O OOO..OOO ..O..O.. ..OOOO..
:crown (p12) This is composed of two caterers, a HW emulator and a T-tetromino. There is some freedom in the placement of the caterers, and they can also be replaced by jams.
.......OO....OO....OO.... ......O..O.O....O.O..O... ......OOO..........OOO... .........OO......OO...... ........O..OOOOOO..O..... ........OO........OO..... ......................... .....O................... OOOO...O...........O..... ...O...O....O....O...OOOO .......O...OOO...O...O... ....O............O....... .....OO.............O.... ..................OO.....
:crucible = cauldron
:cuphook (p3) Found by Rich Schroeppel, late 1970 or early 1971.
....OO... OO.O.O... OO.O..... ...O..... ...O..O.. ....OO.O. .......O. .......OO
:curl = loop
:dart (c/3 ortogonally, p3) Found by David Bell.
.......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.
OO...OO O.O.O.O ..O.O.. O.O.O.O OO...OO
:D-heptomino = Herschel
:diamond = tub
:diamond ring (p3)
......O...... .....O.O..... ....O.O.O.... ....O...O.... ..OO..O..OO.. .O....O....O. O.O.OO.OO.O.O .O....O....O. ..OO..O..OO.. ....O...O.... ....O.O.O.... .....O.O..... ......O......
:diehard Any pattern that vanishes, but only after a long time. The following example (found by myself in April 1998) vanishes in 130 generations, which is probably the limit for patterns of 7 or fewer cells. Note that there is no limit for higher numbers of cells - e.g., for 8 cells we could have a glider heading towards an arbitrarily distant blinker.
......O. OO...... .O...OOO
:dinner table (p12) Found by Robert Wainwright.
.O........... .OOO.......OO ....O......O. ...OO....O.O. .........OO.. ............. .....OOO..... .....OOO..... ..OO......... .O.O....OO... .O......O.... OO.......OOO. ...........O.
:dock The 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.
:double block reaction A certain reaction that can be used to stabilize the twin bees shuttle (qv). This was discovered by David Bell in October 1996. The same reaction sometimes works in other situations, as shown in the following diagram where a pair of blocks eats an R-pentomino and a LWSS.
.OOOO.....OO.... O...O......OO.OO ....O......O..OO O..O............ ................ .............OO. .............OO.
:double head = paperclip
:double wing = moose antlers
:dove The following induction coil.
.OO.. O..O. .O..O ..OOO
:down boat with tail = cis-boat with tail
:drain trap = paperclip
:dual 1-2-3-4 = cloverleaf
:eater Any still life that has the ability to repair itself after suffering certain types of damage. The term is also used specifically to refer to the fishhook.
:eater2 (p1) This still life has essentially the same eating action as the ordinary eater (see fishhook). There are two basic reasons why it is occasionally useful: because of its symmetry it acts like an eater in two directions, and also it takes longer to recover from each bite. This second property means that, among other things, it can eat a glider in a position that would destroy a fishhook. This novel glider-eating action is occasionally of use in itself, and combined with the symmetry means that an eater2 can eat gliders along four different paths.
...O.OO .OOO.OO O...... .OOO.OO ...O.O. ...O.O. ....O..
:eater3 (p1) This large symmetric eater has a very different eating action from the fishhook and eater2. The loaf can take bites out things, being flipped over in the process. The rest of the eater merely flips it back again.
.........OO. ....OO..O..O .O..O....O.O O.O.O.....O. .O..O.OO.... ....O..O.... .....O....O. ......OOOOO. ............ ........O... .......O.O.. ........O...
:eater/block frob (p4) Found by Dave Buckingham.
.OO....... ..O....... ..O.O..... ...O.O.... .....OO.OO ........OO ..OO...... ...O...... OOO....... O.........
O........... OOO......... ...O........ ..OO........ ...OO....... ....OO...... ...O..O..... ...O..OO.... ....OO.OOO.. ........O.O. ..........O. ..........OO
:eater-bound Z-hexomino = pentoad
:eater eating eater = two eaters
:eaters + = French kiss
:ecologist (c/2 orthogonally, p20) This consists of the classic puffer train with a LWSS added to suppress the debris. See also space rake.
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 spark A spark at the side of a spaceship that can be used to perturb things as the spaceship passes by.
:egg = non-spark
:E-heptomino Name given by Conway to the following heptomino.
.OOO OO.. .OO.
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"). Until recently all Herschel loops of period less than 62 were emus, because with lower periods any gliders produced tend to hit the following Herschel and so must be deleted. Progress has recently been made by Dieter Leithner (see Quetzalcoatlus).
: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 possible, but they require stabilizing objects to suppress their non-sparks and so are of little use. The emulators were discovered by Robert Wainwright in 1980.
:Eureka (p30) A shuttle found by Dave Buckingham and Robert Wainwright. See pre-pulsar.
.O..............O. O.O....O.......O.O .O...OO.OO......O. .......O.......... .................. .................. .................. .......O.......... .O...OO.OO......O. O.O....O.......O.O .O..............O.
:exposure = underpopulation
:extremely impressive (p6) Found by Dave Buckingham.
....OO...... ...O.OOO.... ...O....O... OO.O...OO... OO.O.....OO. ....OOOOO..O ..........OO ......O..... .....O.O.... ......O.....
:evolutionary factor For an unstable pattern, the time to stabilization divided by the initial population. For example, the R-pentomino has an evolutionary factor of 220.6, while bunnies has an evolutionary factor of 1925.777... The term is no longer in use.
:factory Another word for gun, but not used in the case of glider guns. The term is also used for a pattern that repeatedly manufactures objects other than spaceships or rakes. In this case the new objects do not move out of the way, and therefore must be used up in some way before the next one is made. The following shows an example of a p144 gun which consists of a p144 block factory whose output is converted into gliders by a p72 oscillator. (This gun was found by Bill Gosper in 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 (4 blinkers), honey farm (4 beehives), blockade (4 blocks), fleet (4 ships, although really 2 ship-ties) and bakery (4 loaves, although really 2 bi-loaves).
:father = parent
:featherweight spaceship = glider
:fencepost Any pattern that stabilizes one end of a wick.
:F-heptomino Name given by Conway to the following heptomino.
OO.. .O.. .O.. .OOO
:figure-8 (p8) Found by Simon Norton.
OOO... OOO... OOO... ...OOO ...OOO ...OOO
:fish A generic term for LWSS, MWSS and HWSS, or, more generally, for any spaceship.
:fishhook (p1) Usually simply called an eater. It was found by Clement Lessner and William Webb. Its ability to eat various objects was discovered by Bill Gosper in 1971.
OO.. O.O. ..O. ..OO
:fleet (p1) A common formation of two ship-ties.
....OO.... ....O.O... .....OO... .......OO. OO.....O.O O.O.....OO .OO....... ...OO..... ...O.O.... ....OO....
:flip-flop Any p2 oscillator. However, the term is also used in two more specific (and non-equivalent) senses: (a) any p2 oscillator whose two phases are mirror images of one another, and (b) any p2 oscillator in which all rotor cells die from underpopulation. In the latter sense it contrasts with on-off. The term has also been used even more specifically for the 12-cell flip-flop shown under phoenix.
:flipper Any oscillator or spaceship that forms its mirror image halfway through its period.
:flotilla A spaceship composed of a number of smaller interacting spaceships. Often one or more of these is not a true spaceship and could not survive without the support of the others. The following example shows an OWSS escorted by two HWSS.
....OOOO....... ...OOOOOO...... ..OO.OOOO...... ...OO.......... ............... ...........OO.. .O............O O.............. O.............O OOOOOOOOOOOOOO. ............... ............... ....OOOO....... ...OOOOOO...... ..OO.OOOO...... ...OO..........
:fly A certain c/3 tagalong found by David Bell, shown here attached to the back of a small spaceship (also by Bell).
..O............................... .O.O.............................. .O.O......................O.O...O. .O.......................OO.O.O..O ...........OOO........O.........O. OO.........OO..O.OO...O..OOOO..... .O.O.........OOOO..O.O..OO....OO.. .OO........O..O...OOO.....OOO..... ..O.......O....O..OO..OO..O..O.... ...O..O...O....O..OOO.O.O....OO... .......O.OO....O..OOOO.....O...... ....OO...OO....O..OOOO.....O...... ....O.O...O....O..OOO.O.O....OO... ...OO.....O....O..OO..OO..O..O.... ....O.O....O..O...OOO.....OOO..... .....O.......OOOO..O.O..OO....OO.. ...........OO..O.OO...O..OOOO..... ...........OOO........O.........O. .........................OO.O.O..O ..........................O.O...O.
:flying machine = Schick engine
:fore and back (p2) Compare snake pit.
OO.OO.. OO.O.O. ......O OOO.OOO O...... .O.O.OO ..OO.OO
:fountain (p4) Found by Dean Hickerson.
.........O......... ................... ...OO.O.....O.OO... ...O.....O.....O... ....OO.OO.OO.OO.... ................... ......OO...OO...... OO...............OO O..O...O.O.O...O..O .OOO.OOOOOOOOO.OOO. ....O....O....O.... ...OO.........OO... ...O...........O... .....O.......O..... ....OO.......OO....
....OO. OO..O.O O.....O .OOOOO. ...O...
:French kiss (p3) Found by Robert Wainwright.
O......... OOO....... ...O...... ..O..OO... ..O....O.. ...OO..O.. ......O... .......OOO .........O
:fumarole (p5) Found by Dean Hickerson.
...OO... .O....O. .O....O. .O....O. ..O..O.. O.O..O.O OO....OO
:fuse A wick burning at one end. For examples, see baker, beacon maker, blinker ship, boat maker, cow, harvester, lightspeed wire, pi ship, reverse fuse, superstring and washerwoman. Useful fuses are usually clean, i.e. they leave behind no debris.
:galaxy = Kok's galaxy
:Game of Life = Life
:Garden of Eden A pattern that has no parent, and so can only occur in generation 0. (This term was first used in connection with cellular automata by John W. Tukey, long before Life was invented.) 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. The following is an example with only 143 on cells.
OO.O.O.O.OO.O. O.OOO.OOO.OO.O OOOO.OOO.OO.O. OOO.O.O.O.OOOO .OOO.O.OOO.OO. OOOOOOO.OOOO.O .O.O.OOOOOOOO. O.OOO.OO.O.O.O OOOOOO.OOOOOO. O.OO.OOOOO.O.O OOO.OOOOOOOOO. .OOO.O.O.O.OOO OOO.O.O.O.OO.O O.OOOOOOOOOOOO
:generation The fundamental unit of time. The starting pattern is generation 0.
: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 Conway's group in 1970 while attempting to track the evolution of the R-pentomino. The name is due in part to the fact that it is glide symmetric.
OOO O.. .O.
:glider construction = glider synthesis
: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 picture shows Dieter Leithner's p44 MWSS gun which he discovered in April 1997 (except that I have mutilated the eater2 to reduce the area). This is the smallest known gliderless gun, and also the smallest known MWSS gun. (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.)
.........OO....OO....OO........................... ........O..O.O....O.O..O.......................... ........OOO..........OOO.......................... ...........OO......OO............................. ..........O..OOOOOO..O............................ ..........OO........OO............................ .................................O................ ...............................OOO................ ..............................O........OOO........ ..............................OO.......O..O....... .........................O.............O.......... ........................O..............O...O...... .........................OO............O.......... ........................O.O.............O.O....... .................................................. .......................O.O.....OOO..............OO ........................O.....O..O...............O OO............OOO.......O......OO...........OO.O.. OO...........O...O..........................OO.OO. .............OO.OO................................ .................................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..OOOOOO..O............................ ...........OO......OO............................. ........OOO..........OOO.......................... ........O..O.O....O.O..O.......................... .........OO....OO....OO...........................
: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. There is an integer n such that every object which has a glider synthesis has an n-glider synthesis (see universal constructor/destructor), but any such n is surely very large. Glider syntheses for all still lifes and known oscillators with at most 14 cells were found by Dave Buckingham.
Perhaps most interesting are glider syntheses of spaceships, because these can be used to create guns firing these spaceships. 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. All other spaceships (except the glider itself, of course) have so far eluded synthesis. Many of them are space dust.
The following diagram shows a 3-glider synthesis of the pentadecathlon. This was found fairly recently 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.
:glide symmetric Undergoing simultaneous reflection and translation. A glide symmetric spaceship is commonly called a flipper.
:GoE = Garden of Eden
:GoL = Game of Life
:Gosper glider gun The first known gun, and indeed the first known finite pattern with unbounded growth, found by Bill Gosper in November 1970. A glider synthesis for this gun is shown under glider synthesis. 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 and Robert Wainwright. Compare with pi portraitor and popover.
..........OO........ ..........O......... ..O.OO.OO.O.....OO.. ..OO.O.O.O......O... ........O........O.. ................OO.. .................... ................OO.. O.........OOO..O.O.. OOO.......O.O...O... ...O......O.O....OOO ..O.O..............O ..OO................ .................... ..OO................ ..O........O........ ...O......O.O.O.OO.. ..OO.....O.OO.OO.O.. .........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.
:grapser = spark coil
:Gray counter (p4) 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.... ......... ..OOOOO.. .O.....O. O.O...O.O .O.....O. ..OOOOO.. ......... ....O.... ...O.O... ....O....
..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.)
:grin The following common parent of the block. The name is not really used in practice - it relates to the infamous Cheshire cat. See also pre-block.
O..O .OO.
: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. See also factory.
: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).
:half bakery See bi-loaf.
:half fleet = ship-tie
:hammer To hammer a LWSS, MWSS or HWSS is to smash things into the rear end of it in order to transform it into a different type of spaceship. A hammer is the object used to do the hammering. In the following example by Dieter Leithner a LWSS is hammered by two more LWSS to make it into a MWSS.
O..O................ ....O...OO.......... O...O..OOO.....OOOO. .OOOO..OO.O....O...O ........OOO....O.... .........O......O..O
:harvester (c p4 fuse) Found by David Poyner, this was the first published example of a fuse. The name refers to the fact the it produces debris in the form of blocks which contain the same number of cells as the fuse has burnt up.
................OO ...............O.O ..............O... .............O.... ............O..... ...........O...... ..........O....... .........O........ ........O......... .......O.......... ......O........... .....O............ OOOOO............. OOOO.............. O.OO..............
:HashLife A Life algorithm that works by storing patterns in a hash table, and using this to jump forward a number of generations at a time. This is very fast, but requires a large amount of memory.
:hassle See hassler.
:hassler An oscillator that works by hassling (repeatedly moving or changing) some object. For some examples, see toadsucker, traffic circle and baker's dozen.
:hat (p1) Found by Charles Corderman.
..O.. .O.O. .O.O. OO.OO
:havoc = mango (This name derives from a diagram in Winning Ways which shows a glider about to hit a mango. The diagram is labelled "Glider causes havoc!".)
:heavyweight emulator = HW emulator
:heavyweight spaceship = HWSS
:heavyweight volcano = HW volcano
:hebdarole (p7) Found by Noam Elkies, November 1997. Compare fumarole. The smaller version shown below was found by Alan Hensel (with a few extra pixels shaved off by myself). The top tens rows can be stabilized by their mirror image (giving an inductor) and this was the original form found by Elkies.
...........OO........... ....OO...O....O...OO.... .O..O..O.O....O.O..O..O. O.O.O.OO.O....O.OO.O.O.O .O..O..O.O.OO.O.O..O..O. ....OO....O..O....OO.... ...........OO........... .......O..O..O..O....... ......O.OO....OO.O...... .......O........O....... ........................ ...OO..............OO... ...O..OOOO....OOOO..O... ....O.O.O.O..O.O.O.O.... ...OO.O...OOOO...O.OO... .......OO......OO....... .........OO..OO......... .........O..O.O......... ..........OO............
:Heisenburp device A pattern which can detect the passage of a glider without affecting the glider's path or timing. The first such device was constructed by David Bell in December 1992.
:heptaplet Any 7-cell polyplet.
:heptapole (p2) The barberpole of length 7.
OO........ O.O....... .......... ..O.O..... .......... ....O.O... .......... ......O.O. .........O ........OO
:heptomino Any 7-cell polyomino. There are 108 such objects. Those with names in common use are the B-heptomino, the Herschel and the pi-heptomino.
:Herschel (stabilizes at time 128) The following pattern which occurs at generation 20 of the B-heptomino.
O.. OOO O.O ..O
:Herschel conduit A conduit that moves a Herschel from one place to another.
:Herschel loop A cyclic Herschel track.
:Herschel track A track for Herschels. See also B track.
:Hertz oscillator (p8) Compare negentropy, and also cauldron. Found by Conway's group.
...OO.O.... ...O.OO.... ........... ....OOO.... ...O.O.O.OO ...O...O.OO OO.O...O... OO.O...O... ....OOO.... ........... ....OO.O... ....O.OO...
:hexadecimal = beehive and dock
:hexaplet Any 6-cell polyplet.
:hexapole (p2) The barberpole of length 6.
OO....... O.O...... ......... ..O.O.... ......... ....O.O.. ......... ......O.O .......OO
:hexomino Any 6-cell polyomino. There are 35 such objects. For some examples see century, stairstep hexomino, table, toad and Z-hexomino.
:H-heptomino Name given by Conway to the following heptomino.
OO.. .O.. .OOO ..O.
:hive = beehive
:hive-nudger (c/2 orthogonally, p4) A spaceship found by Hartmut Holzwart in 1992. It consists of a pre-beehive escorted by four LWSS. In fact any LWSS can be replaced by a MWSS or a HWSS, so that there are 45 different single-hive hive-nudgers.
OOOO.....O..O O...O...O.... O.......O...O .O..O...OOOO. ............. .....OO...... .....OO...... .....OO...... ............. .O..O...OOOO. O.......O...O O...O...O.... OOOO.....O..O
..OO.. .O..O. O.OO.O .O..O. ..OO..
:honey farm (p1) A common formation of four beehives.
......O...... .....O.O..... .....O.O..... ......O...... ............. .OO.......OO. O..O.....O..O .OO.......OO. ............. ......O...... .....O.O..... .....O.O..... ......O......
:hook Another term for a bookend. It is also used for other hook-shaped things, such as occur in the fishhook and the hook with tail, for example.
O.O.. OO.O. ...O. ...OO
:house The following induction coil. It is generation 3 of the pi-heptomino. See spark coil and dead spark coil.
.OOO. O...O OO.OO
:hustler (p3)
.....OO.... .....OO.... ........... ...OOOO.... O.O....O... OO.O...O... ...O...O.OO ...O....O.O ....OOOO... ........... ....OO..... ....OO.....
:hustler II (p4)
....O........... ....OOO......... .......O........ ......O..OO..... O.OO.O.OO..O.... OO.O.O.....O.... .....O....O..... ....O.....O.O.OO ....O..OO.O.OO.O .....OO..O...... ........O....... .........OOO.... ...........O....
:HW emulator (p4) See also emulator.
.......OO....... ..OO.O....O.OO.. ..O..........O.. ...OO......OO... OOO..OOOOOO..OOO O..O........O..O .OO..........OO.
:HWSS (c/2 orthogonally, p4) The fourth most common spaceship. Found by Conway, 1970.
...OO.. .O....O O...... O.....O OOOOOO.
:HWSS emulator = HW emulator
:HW volcano (p5) A p5 domino sparker. There are at least two known forms for this, one of which is shown below.
.........O.......................... ........O.O......................... ......OOO.O......................... .....O....OO.O...................... .....O.OO...OO......OO.............. ....OO.O.OO.........O.O............. .........O.OOOOO......O..O.OO....... ..O.OO.OO.O.....O....OO.O.OO.O...... .....OO.....OOOO........O....O...... O...O.O..O...O.O....OO.O.OOOO.OO.... O...O.O..OO.O.OO.OO....O.O....O.O... .....OO...OOO.OO.O.OOO.O..OOO...O... ..O.OO.OO.OO.............O.O..O.O.OO ...........O......O.O.O.O..OO.O.O.O. ....OO.O.O.OO......OO.O.O.O...O.O.O. .....O.OO.O..O.......O.OO..OOOO.OO.. .....O....O.O........O...OO......... ....OO....OO........OO...O..O....... ...........................OO.......
:I-heptomino Name given by Conway to the following heptomino.
OO.. .O.. .OO. ..OO
:induction coil Any object used to stabilize an edge (or edges) without touching. The tubs used in the Gray counter are examples, as are the blocks and snakes used in the Hertz oscillator and the heptomino at the bottom of the mathematician.
:inductor Any oscillator with a row of dead cells down the middle and whose two halves are mirror images of one another, both halves being required for the oscillator to work. Examples are the pulsar and the tumbler. If still lifes are considered as p1 oscillators then there are numerous simple examples such as table on table, dead spark coil and cis-mirrored R-bee. Some spaceships, such as the brain, the snail and the spider use the same principle.
:infinite growth Growth of a finite pattern such that the population tends to infinity, or at least is unbounded. The first known pattern with infinite growth was the Gosper glider gun. An interesting question is: What is the minimum population of a pattern that exhibits infinite growth? In 1971 Charles Corderman found that a switch engine could be stabilized by a pre-block in a number of different ways, giving 11-cell patterns with infinite growth. This record stood for more than quarter of a century until Paul Callahan found, in November 1997, two 10-cell patterns with infinite growth. The following month he found the one shown below, which is much neater, being a single cluster. This produces a stabilized switch engine of the block-laying type.
......O. ....O.OO ....O.O. ....O... ..O..... O.O.....Nick Gotts and Paul Callahan have also shown that there is no infinite growth pattern with fewer than 10 cells, so that the question has now been answered.
Also of interest is the following pattern (again found by Callahan), which is the only 5x5 pattern with infinite growth. This too emits a block-laying switch engine.
OOO.O O.... ...OO .OO.O O.O.OFollowing a conjecture of Nick Gotts, Stephen Silver produced, in May 1998, a pattern of width 1 which exhibits infinite growth. Again the pattern relies on switch engines. (This pattern is far too big to show here, being 1x5447. At a guess I would say this could be reduced a hundredfold if someone were to apply enough computing power to an exhaustive search.)
Although the simplest infinite growth patterns grow at a rate that is (asymptotically) linear, many other types of growth rate are possible, quadratic growth (see breeder) being the fastest. Dean Hickerson has found many patterns with unusual growth rates (such as sawtooths).
:integral = integral sign
...OO ..O.O ..O.. O.O.. OO...
:intentionless = elevener
:interchange (p2) A common formation of six blinkers.
..OOO....OOO.. .............. O............O O............O O............O .............. ..OOO....OOO..
:island The unconnected polyplets of which a stable pattern consists are sometimes called islands. So, for example, a boat has only one island, while a bi-block has two, a honey farm has four and the standard form of the eater3 has five.
:jack (p4)
...O.....O... ...OO...OO... O..OO...OO..O OOO..O.O..OOO .....O.O..... OOO..O.O..OOO O..OO...OO..O ...OO...OO... ...O.....O...
:jam (p3) Found by Dean Hickerson. Compare with mold. In fact this is really very like caterer.
...OO. ..O..O O..O.O O...O. O..... ...O.. .OO...
:Jaws A breeder constructed by Nick Gotts in February 1997. Jaws has the smallest population of any known pattern with superlinear growth. This was 150 cells in the original version, reduced by Gotts to 130 in November 1997 using some switch engine predecessors found by Paul Callahan. Jaws consists of eight pairs of switch engines which produce a block-laying switch engine (plus masses of junk) every 10752 generations. It is therefore an MMS breeder, although not of the simple puffer puffer variety.
:JC = dead spark coil
:JHC = monogram (Note that these are the initials of Life's creator.)
:J-heptomino = Herschel
:Jolson = Al Jolson
:keys (p3)
....O..O.... .O..O..O..O. O.OOO..OOO.O .O........O.
:kickback reaction The following collision of two gliders whose product is a single glider travelling in the opposite direction to one of the original gliders. This is important in the proof of the existence of a universal constructor/destructor, and in Bill Gosper's total aperiodic, as well as a number of other constructions.
.....O.. ......OO .OO..OO. O.O..... ..O.....
:knightship Any spaceship that moves two cells vertically for every one cell that it moves horizontally (or vice versa). Such spaceships do exist (see universal constructor/destructor), but no concrete example is known.
:Kok's galaxy (p8) Found by Jan Kok in 1971.
OOOOOO.OO OOOOOO.OO .......OO OO.....OO OO.....OO OO.....OO OO....... OO.OOOOOO OO.OOOOOO
:lake Any still life consisting of a simple closed curve made from diagonally connected dominoes. The smallest example is the pond, and the next smallest is this (to which the term is sometimes restricted):
....OO.... ...O..O... ...O..O... .OO....OO. O........O O........O .OO....OO. ...O..O... ...O..O... ....OO....
:large S = big S
:Life A 2-dimensional 2-state cellular automaton discovered by John Conway in 1970. The states are referred to as ON and OFF (or live and dead). The transistion rule is as follows: a cell that is ON will remain ON in the next generation if and only if exactly two or three of the eight adjacent cells are also ON, and a cell that is OFF will turn ON if and only if exactly three of the eight adjacent cells are ON.
:LifeLine A newletter edited by Robert Wainwright from 1971 to 1973. During this period it was the main forum for discussions about Life. The newletter was nominally quarterly, but the actual dates of its eleven issues were as follows:
Mar, Jun, Sep, Dec 1971 Sep, Oct, Nov, Dec 1972 Mar, Jun, Sep 1973
:Lifenthusiast A Life enthusiast. Term coined by Robert Wainwright.
:lifesrc David Bell's Life search program, for finding new spaceships and oscillators. This is a C implementation of an algorithm developed by Dean Hickerson in 6502 assembler. Most of the spaceships and many of the oscillators shown in this lexicon were found with lifesrc or by Hickerson's original program.
.OO.O.. .O.OO.. ....... ..OOO.. .O...O. .O...O. ..O.O.. O.O.O.O OO...OO
:lightspeed wire Any wick that can burn non-destructively at the speed of light. These are potentially useful for various things, but so far no-one has found the necessary mechanisms. The following example shows an example of a lightspeed wire, with a small defect that travels along it at the speed of light.
..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O.. ..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.. ........................................................... ..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.. .O......O................................................O. O.OOOOO....OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.O .O.....O.................................................O. ..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.. ........................................................... ..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.. ..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O..O..
:lightweight emulator = LW emulator
:lightweight spaceship = LWSS
:lightweight volcano = toaster
:line puffer A puffer which produces its output by means of an orthogonal line of cells at right angles to the direction of travel. The first example (actually a spaceship) was found by Alan Hensel in March 1994, based on a spaceship found earlier that month by Hartmut Holzwart. Hensel found a way to make extensible line puffers, but in October 1995 Tim Coe discovered that these were often unstable, although typically lasting millions of generations. By May 1996, however, Coe had found a way to fix the instability. The resulting puffers appear to be completely stable and to exhibit an exponential increase in period as a function of width, although neither of these things have been proved.
.OO. O..O .O.O ..O.
:loaf on loaf = bi-loaf
:loaf p3 = jam
:loaf pendel = mold
:LoM = lumps of muck
:lonely bee = worker bee
.O... O.O.. .O.O. ..O.O ...O.
:long boat (p1)
.O.. O.O. .O.O ..OO
:long bookend The following induction coil.
...OO O...O OOOO.
....OO .....O ....O. ...O.. O.O... OO....
:long hat = loop
:long hook = long bookend
:long house = dock
:long integral (p1)
..OO .O.O .O.. ..O. O.O. OO..
:long long barge = very long barge
:long long boat = very long boat
:long long ship = very long ship
:long long canoe = very long canoe
:long long snake = very long snake
:long ship (p1)
OO.. O.O. .O.O ..OO
:long sinking ship = long canoe (p1)
OO... O.O.O ...OO
..OO. .O..O .O.O. OO.OO
:low-denisty Life = sparse Life
:lumps of muck The common evolutionary sequence that ends in the blockade. The name is sometimes used of the blockade itself, and can in general be used of any stage of the stairstep hexomino.
:LW emulator (p4) The smallest emulator.
..OO.O..O.OO.. ..O........O.. ...OO....OO... OOO..OOOO..OOO O..O......O..O .OO........OO.
:LWSS (c/2 orthogonally, p4) The smallest orthogonally moving spaceship, and the second most common (after the glider). Found by Conway, 1970.
.O..O O.... O...O OOOO
:LWSS emulator = LW emulator
:LW volcano = toaster
.OO.. O..O. .O..O ..OO.
:mathematician (p5) Found by Dave Buckingham.
....O.... ...O.O... ...O.O... ..OO.OO.. O.......O OOO...OOO ......... OOOOOOOOO O.......O ...OOOO.. ...O..OO.
:mazing (p4)
...OO.. .O.O... O.....O .O...OO ....... ...O.O. ....O..
:medium fish = MWSS
:methuselah Any small pattern that stabilizes only after a long time. Term coined by Conway. Examples include the R-pentomino, acorn and bunnies.
:middleweight emulator = MW emulator
:middleweight spaceship = MWSS
:middleweight volcano = MW volcano
:M.I.P. value The maximum population divided by the initial population for an unstable pattern. For example, the R-pentomino has an M.I.P. value of 63.8, since its maximum population is 319. The term is no longer in use.
:MIT oscillator = cuphook
:MMM breeder See breeder.
:MMS breeder See breeder.
:mold (p4) Found by Achim Flammenkamp in 1988 and independently by Dean Hickerson in 1990. Compare with jam.
...OO. ..O..O O..O.O ....O. O.OO.. .O....
:monogram (p4) Found by Dean Hickerson.
OO...OO .O.O.O. .OO.OO. .O.O.O. OO...OO
OO.....OO O.......O .OOO.OOO. ...O.O... ....O....
:mould = mold
:MSM breeder See breeder.
:multum in parvo (stabilizes at time 3933) A methuselah found by Charles Corderman, but not as long-lasting as his acorn.
...OOO ..O..O .O.... O.....
:muttering moat Any oscillator whose rotor consists of a closed chain of cells each of which is adjacent to exactly two other rotor cells. Compare babbling brook. Examples include the blinker, the clock, the cuphook, the Gray counter and the scrubber. The following diagram shows a p2 example with a much larger rotor.
....O.O.... ..O..O..O.. ...O.O.O... .OOO.O.OOO. .....O..... OOOOO.OOOOO .....O..... .OOO.O.OOO. ...O.O.O... ..O..O..O.. ....O.O....
:MW emulator (p4) See also emulator.
.......O....... ..OO.O...O.OO.. ..O.........O.. ...OO.....OO... OOO..OOOOO..OOO O..O.......O..O .OO.........OO.
:MWSS (c/2 orthogonally, p4) The third most common spaceship. Found by Conway, 1970.
...O.. .O...O O..... O....O OOOOO.
:MWSS emulator = MW emulator
:MWSS out of the blue The following reaction, found by Peter Rott in November 1997, in which a LWSS passing by a p46 oscillator creates a MWSS travelling in the opposite direction. Together with some reactions found by Dieter Leithner, and a LWSS-turning reaction found earlier by Paul Callahan, this can be used to prove that there exist gliderless guns for LWSS, MWSS and HWSS for all periods that are multiples of 46.
O..O................................. ....O................................ O...O................................ .OOOO................................ ..................................... ..................................... ..................................... ..................................... ..................................... ...................OO..............OO ..................OO...............OO ...................OOOOO............. ..OO................OOOO............. ..OO.....O........................... ........OOO.........OOOO............. .......O.O.O.......OOOOO............. ........O..O......OO...............OO ........OOO........OO..............OO .........O........................... ..................................... ..................................... ..................................... ..................................... ..O.......O.......................... ..................................... OOO.......OOO........................ .OO.OO.OO.OO......................... ..OOO...OOO.......................... ...O.....O........................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..................................... ..OO.....OO.......................... ..OO.....OO..........................
:MW volcano (p5) Found by Dean Hickerson.
......O...... ....O...O.... ............. ...O.....O... .OOO.OOO.OOO. O...OO.OO...O O.OOO.O.OOOO. .O........... ...O.O.O.OO.O ..OO.OOO.O.OO ...O.O..O.... ...O..OO..... ..OO.........
:My Experience with B-heptominos in Oscillators An article by Dave Buckingham (October 1996) that described his discovery of Herschel conduits, including sufficient (indeed ample) stable conduits to enable, for the first time, the construction of period n oscillators - and true period n guns - for every sufficiently large integer n (61, later reduced to 59, for oscillators, and 62 for guns).
:natural Occurring often in random patterns. There is no precise measure of naturalness, since the most useful definition of "random" in this context is open to debate. Nonetheless, it is clear that objects such as blocks, blinkers, beehives and gliders are very natural, while eater2s, darts, guns, etc., are not.
:negentropy (p2) Compare Hertz oscillator.
...OO.O.... ...O.OO.... ........... ....OOO.... ...O.O.O.OO ...OO..O.OO OO.O...O... OO.O...O... ....OOO.... ........... ....OO.O... ....O.OO...
:neighbour Any of the eight cells adjacent to a given cell. A cell is therefore not considered to be a neighbour of itself, although the neighbourhood used in Life does in fact include this cell (see cellular automaton).
:new gun An old name for the second known basic gun (found, like the first, by Bill Gosper), shown below. A number of other ways of constructing a gun from two twin bees shuttles have since been found.
.........................OO.....OO .........................OO.....OO .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. ...........................OO.OO.. ..........................O.....O. .................................. .........................O.......O .........................O..O.O..O .........................OOO...OOO .................................. .................................. .................................. .................................. .................O................ OO...............OO............... OO................OO.............. .............OO..OO............... .................................. .................................. .................................. .............OO..OO............... OO................OO.......OO..... OO...............OO........OO..... .................O................
:Noah's ark The following diagonal puffer consisting of two switch engines. The name comes from the variety of objects it leaves behind: blocks, blinkers, beehives, loaves, gliders, ships boats, long boats, beacons and block on tables.
..........O.O.. .........O..... ..........O..O. ............OOO ............... ............... ............... ............... ............... .O............. O.O............ ............... O..O........... ..OO........... ...O...........
:n-omino Any polyomino with exactly n cells.
:non-spark Something that looks like a spark, but isn't. An OWSS produces one of these instead of a belly spark, and is destroyed by it.
:non-standard spaceship Any spaceship other than a glider, LWSS, MWSS or HWSS.
:octagon II (p5) The first known p5 oscillator, discovered (late 1970 or early 1971) independently by Sol Goodman and Arthur Taber. The name is due to the latter.
...OO... ..O..O.. .O....O. O......O O......O .O....O. ..O..O.. ...OO...
:omniperiodic A cellular automaton is said to be omniperiodic if it has oscillators of all periods. It is not known if Life is omniperiodic, although this seems likely. Dave Buckingham's work on Herschel conduits (see My Experience with B-heptominos in Oscillators) reduced the number of unresolved cases to a finite number. At the time of writing the only periods for which no oscillator is known are 19, 23, 27, 31, 37, 38, 41, 43, 49 and 53. (However, for periods 33, 34, 39 and 51 the known examples are very unsatisfactory, consisting merely of the juxtaposition of lower period oscillators without any interaction between the rotors.)
:on-off Any p2 oscillator in which all rotor cells die from overpopulation. The simplest example is a beacon. Compare flip-flop.
:O-pentomino Conway's name for the following pentomino.
OOOOO
:Orion (c/4 diagonally, p4) The smallest known diagonal spaceship other than the glider. Found by Hartmut Holzwart, July 1993.
...OO......... ...O.O........ ...O.......... OO.O.......... O....O........ O.OO......OOO. .....OOO....OO ......OOO.O.O. .............O ......O.O..... .....OO.O..... ......O....... ....OO.O...... .......O...... .....OO.......
:orphan = Garden of Eden
:oscillator Any pattern that is a predecessor of itself. The term is usually restricted to finite patterns. It is usual also to exclude still lifes. See also omniperiodic.
:overcrowding = overpopulation
:overpopulation Death of cell caused by it having more than three neighbours.
:overweight spaceship = OWSS
:OWSS A would-be spaceship similar to LWSS, MWSS and HWSS but longer. On its own an OWSS is unstable, but it can be escorted by true spaceships to form a flotilla.
:Ox A 1976 novel by Piers Anthony which involves Life.
:p = period
:p30 shuttle = queen bee shuttle
:p46 shuttle = twin bees shuttle
:p54 shuttle (p54) A surprising variant of the twin bees shuttle found by Dave Buckingham in 1973. See also centinal.
OO.........................OO .O.........................O. .O.O.......O.............O.O. ..OO.....O..O.....O......OO.. ............O.....OO......... ........O..........OO........ ........O...OO....OO......... .........OOOOO............... ............................. .........OOOOO............... ........O...OO....OO......... ........O..........OO........ ............O.....OO......... ..OO.....O..O.....O......OO.. .O.O.......O.............O.O. .O.........................O. OO.........................OO
:pair of bookends = bookends
:pair of tables = table on table
..OO. .O..O .O.OO OO.O. O..O. .OO..
:parent A pattern is said to be a parent of the pattern it gives rise to after one generation. Some patterns have infinitely many parents, but other have none at all (see Garden of Eden).
:PD = pentadecathlon
:pedestle (p5)
.....O..... ....O.O.... .O..OO..... .OOO....... .....OOO... ...OO...O.. ..O....O..O .O.O.O.O.OO .O.O...O.O. OO.O.O.O.O. O..O....O.. ..O...OO... ...OOO..... .......OOO. .....OO..O. ....O.O.... .....O.....
:penny lane (p4)
...OO.....OO... ...O.......O... OO.O.......O.OO OO.O.OOOOO.O.OO ....O..O..O.... .....OOOOO..... ............... .......O....... ......O.O...... .......O.......
:pentadecathlon (p15) Found by Conway while tracking the history of short rows of cells - 10 cells giving this object, which is the most natural oscillator of period greater than 3.
..O....O.. OO.OOOO.OO ..O....O..
:pentant (p5) Found by Robert Wainwright.
OO........ .O........ .O.O...... ..OO....OO .........O .....OOOO. .....O.... ..O...OOO. ..OOOO..O. .....O.... ....O..... ....OO....
:pentaplet Any 5-cell polyplet.
:pentapole (p2) The barberpole of length 5.
OO...... O.O..... ........ ..O.O... ........ ....O.O. .......O ......OO
:pentoad (p5) Found by Bill Gosper. This is extensible: if an eater is moved back four spaces then another Z-hexomino can can be inserted.
...........OO ...........O. .........O.O. .........OO.. .....OO...... ......O...... ......O...... ......OO..... ..OO......... .O.O......... .O........... OO...........
:pentomino Any 5-cell polyomino. There are 12 such patterns, and Conway assigned them all letters in the range O to Z, loosely based on their shapes. Only in the case of the R-pentomino has Conway's label remained in common use, but all of them can nonetheless be found in this lexicon.
:period The smallest number of generations it takes for an oscillator or spaceship to reappear in its original form. The term can also be used for a puffer, wick, fuse, stream of spaceships, factory or gun. In the last case there is a distinction between true period and pseudo period.
:phi The following common spark. The name comes from the shape in the generation after the one shown here.
.OOO. O...O O...O .OOO.
:phoenix Any pattern all of whose cells die in every generation, but which never dies as a whole. In fact it can be proved that a spaceship cannot be a phoenix, so the term applies mainly to oscillators, of which the following is the smallest (and is sometimes simply called "the phoenix").
....O... ..O.O... ......O. OO...... ......OO .O...... ...O.O.. ...O....
:pi = pi-heptomino
:pi-heptomino (stabilizes at time 173) A common pattern. The name is also applied to later generations of this object - in a pi ship, for example, the pi-heptomino itself never arises.
OOO O.O O.O
:pincers = great on-off
:pinwheel (p4) Found by Simon Norton. Compare clock II.
......OO.... ......OO.... ............ ....OOOO.... OO.O....O... OO.O..O.O... ...O...OO.OO ...O.O..O.OO ....OOOO.... ............ ....OO...... ....OO......
:pi portraitor (p32) Found by Robert Wainwright. Compare with gourmet and popover.
...........OO........... ......OO.O....O.OO...... ......O..........O...... .......OO......OO....... ....OOO..OOOOOO..OOO.... ....O..O........O..O.... .OO.O.O..........O.O.OO. .O.O.O............O.O.O. ...O................O... .O..O..............O..O. ....O.......OOO....O.... O...O.......O.O....O...O O...O.......O.O....O...O ....O..............O.... .O..O..............O..O. ...O................O... .O.O.O............O.O.O. .OO.O.O..........O.O.OO. ....O..O........O..O.... ....OOO..OOOOOO..OOO.... .......OO......OO....... ......O..........O...... ......OO.O....O.OO...... ...........OO...........
:pipsquirt = pipsquirter
:pipsquirter An oscillator that produces a domino spark that is orientated parallel to the direction from which it is produced (in contrast to domino sparkers like the pentadecathlon and HWSS, which produce domino sparks perpendicular to the direction of production). The following is a small p6 example found by Noam Elkies in November 1997.
.....O......... .....O......... ............... ...O...O....... .OOO.O.OOO..... O...OO....O.... O.OO..OO.O.O... .O..OO..OO.O... ..OO..OO.O.O.OO ....O..O.O.O.OO ....OOOO.OO.... ........O...... ......O.O...... ......OO.......
:pi ship A growing spaceship in which the back part consists of a pi-heptomino travelling at a speed of 3c/10. The first example was constructed by David Bell. All known pi ships are too large to show here, but the following diagram shows how the pi fuse works.
............O............ ...........O.O........... OO........OO.OO........OO OO.....................OO
:piston = shuttle
:pixel = cell
:plet = polyplet
:polyomino A finite collection of orthogonally connected cells. The mathematical study of polyominoes was initiated by Solomon Golomb in 1953. Conway's early investigations of Life and other cellular automata involved tracking the histories of small polyominoes, this being a reasonable way to ascertain the typical behaviour of different cellular automata using the limited computing power then available. Polyominoes have no special significance in Life, but their extensive study during the early years lead to a number of important discoveries and has influenced the terminology of Life. (Note on spelling: As with "dominoes" the plural may also be spelt without an e. In this lexicon I have followed Golomb in using the longer form.)
:polyplet A finite collection of orthogonally or diagonally connected cells. This king-wise connectivity is a more natural concept in Life than the orthogonal connectivity of the polyomino.
.OO. O..O O..O .OO.
:pond on pond (p1) This term is often used to mean bi-pond, but may also be used of the following pseudo still life.
.OO...OO. O..O.O..O O..O.O..O .OO...OO.
:popover (p32) Found by Robert Wainwright. Compare with gourmet and pi portraitor.
.....................O.......... .....................O.......... .....................OOO........ .............OO.......OO........ .............OO..OOO..OO........ ...................OOO.......... ...................OOO.......... ..............OO................ ..OOO........O..O............... ..OOO........O.O................ OOO..OO...O...O....OOO.......... .....OO...O..................... ....OOO...O..................... ....O.................OO...OO... ....O...........OOO..O..O..OO... ........O.......O.O...O.O....... .......O.O......O.O....O........ ...OO..O..O................O.... ...OO...OO.................O.... .....................O...OOO.... .....................O...OO..... ..........OOO........O...OO..OOO .................OO........OOO.. ................O..O.......OOO.. ................O.O............. ..........OOO....O.............. ..........OOO................... ........OO..OOO..OO............. ........OO.......OO............. ........OOO..................... ..........O..................... ..........O.....................
:population The number of ON cells.
:P-pentomino Conway's name for the following pentomino.
OO OO O.
:pre-beehive The following common parent of the beehive.
OOO OOO
:pre-block The following common parent of the block. Another such pattern is the grin.
O. OO
:precursor = predecessor
:predecessor Any pattern that evolves into a given pattern after one or more generations.
:pre-pulsar A common predecessor of the pulsar, such as that shown below. This duplicates itself in 15 generations. (It fails, however, to be a replicator because of the way the two copies then interact.) A pair of tubs can be placed to eat half the pre-pulsar as it replicates; this gives the p30 oscillator Eureka where the pre-pulsar's replication becomes a movement back and forth. (See twirling T-tetsons II for a variation on this idea.) By other means the replication of the pre-pulsar can be made to occur in just 14 generations as half of it is eaten; this allows the construction of p28 and p29 oscillators, and is in fact the only known method for creating a p29 oscillator. The pre-pulsar is also a vital component of the only known p47 oscillator. In late 1997 Noam Elkies found that a pre-pulsar can also act as a tagalong pulled by a pair of Tim Coe's large p5 c/5 spaceships, thereby giving a p15 c/5 spaceship. In May 1998 David Bell took this idea further using spiders.
OOO...OOO O.O...O.O OOO...OOO
.....O..... ....O.O.... ....O.O.... ...OO.OO... O.O.....O.O OO.O.O.O.OO ...O...O... ...O...O... ....OOO.... ........... ...O.OO.... ...OO.O....
:pseudo Opposite of true. A gun emitting a period n stream of spaceships (or rakes) is said to be a pseudo period n gun if its mechanism oscillates with a period different from n. This period will necessarily be a multiple of n. Pseudo period n glider guns are known to exist for all periods greater than 13. (Gliders cannot travel in a stream of period 13 or less, so this result is the best possible.)
:pseudo-barberpole (p5) Found by Achim Flammenkamp.
..........OO ...........O .........O.. .......O.O.. ............ .....O.O.... ............ ...O.O...... ............ ..OO........ O........... OO..........
:pseudo still life The strict definition of still life rules out such stable patterns as the bi-block. In such patterns there are dead cells which have more than 3 neigbours in total, but fewer than 3 in any component still life. These patterns are called pseudo still lifes. Mark Niemiec has enumerated the pseudo still lifes up to 24 bits, and his figures are shown below.
8 1 9 1 10 7 11 16 12 55 13 110 14 279 15 620 16 1645 17 4067 18 10843 19 27250 20 70637 21 179011 22 462086 23 1184882 24 3068984
:puffer An object that moves like a spaceship, except that it leaves debris behind. The first known puffers were found by Bill Gosper and travelled at c/2 orthogonally. Not long afterwards c/12 diagonal puffers were found (see switch engine). Discounting wickstretchers (which are not puffers in the conventional sense), no new speed or direction was attained after this until David Bell found the first c/3 orthogonal puffer in April 1996. Since then c/5 orthogonal puffers have also been found, the first by Tim Coe in 1997.
:puffer engine A pattern which can be used as the main component of a puffer. The pattern may itself be a puffer (e.g. the classic puffer train), it may be a spaceship (e.g. the Schick engine), or it may even be unstable (e.g. the switch engine).
:puffer train The full name for a puffer, coined by Conway before any examples were known. The term was also applied specifically to the classic puffer train found by Bill Gosper and shown below. This is very dirty, and the tail does not stabilize until generation 5533. It consists of a B-heptomino (shown here one generation before the standard form) escorted by two LWSS.
.O........O....O.. O.....O..O....O... O......OOO....O... O..O..........O..O OOO...........OOO.
:pulsar (p3) Despite its size, this is the fourth most common oscillator (and by far the most common of period greater than 2) and was found very early on by Conway. See also pre-pulsar and pulsar quadrant.
..OOO...OOO.. ............. O....O.O....O O....O.O....O O....O.O....O ..OOO...OOO.. ............. ..OOO...OOO.. O....O.O....O O....O.O....O O....O.O....O ............. ..OOO...OOO..
:pulsar CP 48-56-72 = pulsar (The numbers refer to the populations of the three phases.)
:pulsar quadrant (p3) This consists of a quarter of the outer part of a pulsar stabilized by a cis fuse with two tails. This is reminiscent of mold and jam. See also two pulsar quadrants.
.....O.. ...OOO.. ..O...OO O..O..O. O...O.O. O....O.. ........ ..OOO...
:pure glider generator A pattern that evolves into one or more gliders, and nothing else. There was some interest in these early on, but they are no longer considered important.
:pushalong Any tagalong at the front of a spaceship. The following is a large example (found by David Bell) attached to the front of a dart.
.........O...O.......................................... ........OO..O.O...........O........O...OO....O.OO.....O. ......O.O.....O..........O.O......O.O..OOO.O.O.......O.O ......OOO.OO.OOO.O.......O........O..O....OOO...O...OO.. ......O.O..OO..OO.O.....O..O......O.OOOOOO.O...........O ..........OOO.......O...OO.O.OO............O.......O...O ..O.OO.O...O....OOO..OO......O..O.OOO...OO.OO...O..O.... .O.OO.OOOOOO.....OOO..OOOO....OO..OOO....O.OO..O.O..OOOO OO.OO................OOO.O.......OOO......OOO.O..O...... .O.OO.OOOOOO.....OOO..OOOO....OO..OOO....O.OO..O.O..OOOO ..O.OO.O...O....OOO..OO......O..O.OOO...OO.OO...O..O.... ..........OOO.......O...OO.O.OO............O.......O...O ......O.O..OO..OO.O.....O..O......O.OOOOOO.O...........O ......OOO.OO.OOO.O.......O........O..O....OOO...O...OO.. ......O.O.....O..........O.O......O.O..OOO.O.O.......O.O ........OO..O.O...........O........O...OO....O.OO.....O. .........O...O..........................................
.......O........ .....OOOOO...... ....O.....O..... .O..O.O.OO.O.... O.O.O.O....O..O. .O..O....O.O.O.O ....O.OO.O.O..O. .....O.....O.... ......OOOOO..... ........O.......
:pyrotechneczum A common, but mistaken, spelling of pyrotechnecium.
:python = long snake
:Q-gun = Quetzalcoatlus
:Q-pentomino Conway's name for the following pentomino.
OOOO ...O
OO..OO O..O.O .O.... ....O. O.O..O OO..OO
:quadpole (p2) The barberpole of length 4.
OO..... O.O.... ....... ..O.O.. ....... ....O.O .....OO
:quapole = quadpole
:queen bee shuttle (p30) Found by Bill Gosper. There are a number of ways to stabilize the ends. Two methods are shown here; for a third see buckaroo. The queen bee shuttle is the basis of the Gosper glider gun.
.........O............ .......O.O............ ......O.O............. OO...O..O............. OO....O.O............. .......O.O........OO.. .........O........O.O. ....................O. ....................OO
:Quetzal = Quetzalcoatlus
:Quetzalcoatlus Dieter Leithner's name for the true p54 glider gun he found in January 1998. (Quetzalcoatlus is the name of a giant flying dinosaur. Leithner's gun is a large Herschel loop which, despite its low period, is not an emu.) Shortly afterwards Leithner built a p56 Quetzal using a mechanism found by Noam Elkies for this purpose.
:R = R-pentomino
:R2D2 (p8) This was found, in the form shown below, by Peter Raynham in the early 1970's. The name derives from a form with a larger and less symmetric stator discovered by Noam Elkies in August 1994. Compare with Gray counter.
....OO.... ....OO.... .......... ..OOOOOO.. .O......O. O.O...OO.O .O......O. ..OOOOOO.. .......... ....OO.... ....OO....
:r5 = R-pentomino
:rabbits (stabilizes at time 17331) A methuselah found by Andrew Trevorrow in 1986.
O...OOO OOO..O. .O.....
:rake Any puffer whose debris consists of spaceships. For examples see space rake and total aperiodic.
:$rats (p6) Found by Dave Buckingham.
.....OO..... ......O..... ....O....... OO.O.OOOO... OO.O.....O.O ...O..OOO.OO ...O....O... ....OOO.O... .......O.... ......O..... ......OO....
:reflector See stable reflector.
:relay Any oscillator in which spaceships (typically gliders) travel in a loop. The simplest example is the p60 one shown below using two pentadecathlons. Pulling the pentadecathlons further apart allows any period of the form 60+120n to be achieved, and this is probably the simplest proof of the existence of oscillators of arbitrarily large period.
...........................O....O.. ................OO.......OO.OOOO.OO .................OO........O....O.. ................O.................. ..O....O........................... OO.OOOO.OO......................... ..O....O...........................
:rephaser The following method of shifting the phase and path of a pair of gliders.
..O..O.. O.O..O.O .OO..OO. ........ ........ ...OO... ...OO...
:replicator A finite pattern which repeatedly creates copies of itself. Such objects are known to exist (see universal constructor/destructor), but no concrete example is known.
:reverse fuse A fuse that produces some initial debris, but then burns cleanly. The following is a simple example.
.............OO ............O.O ...........O... ..........O.... .........O..... ........O...... .......O....... ......O........ .....O......... ....O.......... ...O........... ..O............ OO............. O..............
:revolver (p2)
O............O OOO....O...OOO ...O.O.O..O... ..O......O.O.. ..O.O......O.. ...O..O.O.O... OOO...O....OOO O............O
:rle Run-length encoded. Run-length encoding is a simple (but not very efficient) method of file compression. In Life the term refers to a specific ASCII encoding used for Life patterns (and patterns for other similar cellular automata). This encoding was introduced by Dave Buckingham and is now the usual means of exchanging Life patterns (especially large ones) by e-mail.
:roteightor (p8) Found by Robert Wainwright.
.O............ .OOO........OO ....O.......O. ...OO.....O.O. ..........OO.. .............. .....OOO...... .....O..O..... .....O........ ..OO..O...O... .O.O......O... .O.......O.... OO........OOO. ............O.
:rotor The cells of an oscillator that change state. Compare stator. It is easy to see that any rotor cell must be adjacent to another rotor cell.
:R-pentomino This is by far the most active polyomino with less than six cells: all the others reach some simple stable form (block, blinker, beehive, traffic light or nothing at all) in at most 10 generations, but the R-pentomino does not stabilize until generation 1103, by which time it has a population of 116.
.OO OO. .O.
:S = big S
:sailboat (p16) Found by Robert Wainwright.
........O...........O........ .......O.O.........O.O....... ........O...........O........ ............................. ......OOOOO.......OOOOO...... .....O....O.......O....O..... ....O..O.............O..O.... .O..O.OO.............OO.O..O. O.O.O.....O.......O.....O.O.O .O..O....O.O.....O.O....O..O. ....OO..O..O.....O..O..OO.... .........OO.......OO......... .............OO.............. .............O.O............. ........O..O..O.............. .......O..................... .....OO..........OOO......... ..O......OO.O....OOO......... .....O...O..O....OOO......... .....OOO.O...O......OOO...... ..O...........O.....OOO...... ...O...O.OOO........OOO...... ....O..O...O................. ....O.OO......O.............. ..........OO................. .........O................... .....O..O....................
:sawtooth Any finite pattern whose population growth is unbounded, but does not tend to infinity. (In other words, the population reaches new heights infinitely often, but also infinitely often drops below some fixed value.) The first such pattern was constructed by Dean Hickerson in April 1991.
:Schick engine (c/2 orthogonally, p12) This spaceship, found by Paul Schick in 1972, produces a large spark (the 15 live cells at the rear in the phase shown below) which can be perturbed by other c/2 spaceships to form a variety of puffers. The diagram below shows the smallest form of the Schick engine, using two LWSS. It is also possible to use two MWSS or two HWSS, or even a LWSS and a HWSS.
OOOO.............. O...O.........O... O...........OO.... .O..O..OO.....OOO. ......OOO......OOO .O..O..OO.....OOO. O...........OO.... O...O.........O... OOOO..............
:Schick ship = Schick engine
:scorpion (p1)
...O... .OOO... O...OO. O.O.O.O .OO.O.O .....O.
....O...... ..OOO...... .O......... .O..OOO.... OO.O...O... ...O...O... ...O...O.OO ....OOO..O. .........O. ......OOO.. ......O....
:SE = switch engine
:SGR = stable glider reflector
:shillelagh (p1)
OO... O..OO .OO.O
:ship (p1) The term is also used as a synonym of spaceship.
OO. O.O .OO
OO.... O.O... .OO... ...OO. ...O.O ....O.
:ship on ship = ship-tie
:ship-tie (p1) The name is by analogy with boat-tie.
OO.... O.O... .OO... ...OO. ...O.O ....OO
:shuttle Any oscillator which consists of an active region moving back and forth between stabilizing objects. The most well-known examples are the queen bee shuttle (which has often been called simply "the shuttle") and the twin bees shuttle. See also p54 shuttle and Eureka. Another example is the p72 R-pentomino shuttle that forms part of the pattern given under factory.
:side Half a sidewalk. In itself this is unstable and requires an induction coil.
OO... O.OOO ....O
:sidecar A small tagalong for a HWSS that was found by Hartmut Holzwart in 1992. The resulting spaceship (shown below) has a phase with only 24 cells, making it in this respect the smallest known spaceship other than the standard spaceships and some trivial two-spaceship flotillas derived from them. Note also that a HWSS can support two sidecars at once.
.O...... O.....O. O.....O. OOOOO.O. ........ ....OO.. ..O....O .O...... .O.....O .OOOOOO.
:side-tracking See universal constructor/destructor.
.OO.OO ..O.O. .O..O. .O.O.. OO.OO.
:siesta (p5) Compare sombreros.
...........OO... ...OO.....O.O... ...O.O....O..... .....O...OO.O... ...O.OO.....OOO. .OOO.....O.O...O O...O.O.....OOO. .OOO.....OO.O... ...O.OO...O..... .....O....O.O... ...O.O.....OO... ...OO...........
:sinking ship = canoe
:skewed quad (p2)
.OO.... .O...OO ..O.O.O ....... O.O.O.. OO...O. ....OO.
:sliding block memory A memory register whose value is stored as the position of a block. The block can be moved by means of glider collisions. In Conway's original formulation (as part of his proof of the existence of a universal computer in Life) 2 gliders were used to pull the block inwards by three diagonal spaces, and 30 gliders were used to push it out by the same amount. Dean Hickerson later greatly improved on this, finding a way to pull a block inwards by one diagonal space using 2 gliders, and push it out using 3 gliders. In order for the memory to be of any use there also has to be a way of reading the value held. It suffices to be able to check if the value is zero (as Conway did), or to be able to detect the transition from one to zero (as Hickerson did).
:small fish = LWSS
:small lake (p1) See also lake.
....O.... ...O.O... ...O.O... .OO...OO. O.......O .OO...OO. ...O.O... ...O.O... ....O....
:smiley (p8) Found by Achim Flammenkamp.
OO.O.OO ...O... O.....O .OOOOO. ....... ....... OOO.OOO
:SMM breeder See breeder.
:snacker (p9) Found by Mark Niemiec. This is a pentadecathlon with stabilizers which force it into a lower period. The stabilizers make the domino spark largely inaccessible, but the snacker is extensible, as shown in the lower diagram, and so a more accessible p9 domino spark can be obtained. In April 1998 Dean Hickerson found an alternative stabilizer that is less obtrusive than the original one, and this is also shown in the second diagram.
OO................OO
.O................O.
.O.O............O.O.
..OO............OO..
.......O....O.......
.....OO.OOOO.OO.....
.......O....O.......
..OO............OO..
.O.O............O.O.
.O................O.
OO................OO
2-engine snacker, showing Dean Hickerson's alternative
stabilization, and the method for extending to any length:
OO................................
.O................................
.O.O.........................OO...
..OO.......................O..O...
.......O....O..............OOO....
.....OO.OOOO.OO...O....O......OOO.
.......O....O...OO.OOOO.OO...O...O
..OO..............O....O......OOO.
.O.O.......................OOO....
.O.........................O..O...
OO...........................OO...
OO.O O.OO
:snake pit This term has been used for two different oscillators.
snake pit (p2) This is essentially fore and back.
O.OO.OO
OO.O.O.
......O
OOO.OOO
O......
.O.O.OO
OO.OO.O
snake pit (p3)
.....OO....
....O..O...
....O.OO...
.OO.O......
O.O.O.OOOO.
O.........O
.OOOO.O.O.O
......O.OO.
...OO.O....
...O..O....
....OO.....
:snail (c/5 orthogonally, p5) The first known c/5 spaceship, discovered by Tim Coe in January 1996.
.O.................................... .O.................................... O..................................... .OOO.................OOO...OOO........ .OO.O.........O...O.O......OOO........ ..O...........OO.O.......O....OOOO.... ......O......O...O.O...OO.O.....OO.... ...O..O.OOO...OO.........O........OO.O ...OO.O.....O.....O.................O. .........O.OOOOOOO.................... ...................................... .........O.OOOOOOO.................... ...OO.O.....O.....O.................O. ...O..O.OOO...OO.........O........OO.O ......O......O...O.O...OO.O.....OO.... ..O...........OO.O.......O....OOOO.... .OO.O.........O...O.O......OOO........ .OOO.................OOO...OOO........ O..................................... .O.................................... .O....................................
:sombreros (p6) If the two halves are moved three spaces closer to one another then the period drops to 4, and the result is just a less compact form of a cloverleaf. Compare also siesta.
...OO........OO... ...O.O......O.O... .....O......O..... ...O.OO....OO.O... .OOO..........OOO. O...O.O....O.O...O .OOO..........OOO. ...O.OO....OO.O... .....O......O..... ...O.O......O.O... ...OO........OO...
:soup A random initial pattern, often assumed to cover the whole Life universe.
:space dust A part of a spaceship or oscillator which looks like a random mix of ON and OFF cells. It is usually very difficult to find a glider synthesis for an object that consists wholly or partly of space dust.
:spacefiller Any pattern that grows at a quadratic rate by filling space with an agar. The first example was found in September 1993 by Hartmut Holzwart, following a suggestion by Alan Hensel. The diagram below shows a smaller spacefiller found by Tim Coe.
..................O........ .................OOO....... ............OOO....OO...... ...........O..OOO..O.OO.... ..........O...O.O..O.O..... ..........O....O.O.O.O.OO.. ............O....O.O...OO.. OOOO.....O.O....O...O.OOO.. O...OO.O.OOO.OO.........OO. O.....OO.....O............. .O..OO.O..O..O.OO.......... .......O.O.O.O.O.O.....OOOO .O..OO.O..O..O..OO.O.OO...O O.....OO...O.O.O...OO.....O O...OO.O.OO..O..O..O.OO..O. OOOO.....O.O.O.O.O.O....... ..........OO.O..O..O.OO..O. .............O.....OO.....O .OO.........OO.OOO.O.OO...O ..OOO.O...O....O.O.....OOOO ..OO...O.O....O............ ..OO.O.O.O.O....O.......... .....O.O..O.O...O.......... ....OO.O..OOO..O........... ......OO....OOO............ .......OOO................. ........O..................
:space rake The following p20 forward glider rake, which was the first known rake. It consists of an ecologist with a LWSS added to turn the dying debris into gliders.
...........OO.....OOOO .........OO.OO...O...O .........OOOO........O ..........OO.....O..O. ...................... ........O............. .......OO........OO... ......O.........O..O.. .......OOOOO....O..O.. ........OOOO...OO.OO.. ...........O....OO.... ...................... ...................... ...................... ..................OOOO O..O.............O...O ....O................O O...O............O..O. .OOOO.................
:spaceship Any finite pattern that reappears (without additions or losses) after a number of generations and displaced by a non-zero amount. By far the most natural spaceships are the glider, LWSS, MWSS and HWSS - no other spaceship has ever been seen to arise from random starting patterns. For further examples see brain, dart, ecologist, flotilla, fly, Orion, pushalong, sidecar, snail, sparky, swan and turtle. It is known that there exist spaceships travelling in all (rational) directions and at arbitrarily slow speeds (see universal constructor/destructor). Before 1989, however, the only known examples travelled at c/4 diagonally (gliders) or c/2 orthogonally (everything else). In 1989 Dean Hickerson started to use automated searches to look for new spaceships. This work, continued by David Bell, Hartmut Holzwart and Tim Coe, has produced a great variety of new spaceships, including orthogonal spaceships of speeds 2c/5, c/3, c/4 and c/5. By different means Hickerson also discovered c/12 diagonal spaceships (see Cordership).
:Spaceships in Conway's Life A series of articles posted by David Bell in August-October 1992 that described many of the new spaceships found by himself, Dean Hickerson and Hartmut Holzwart. Bell produced an addendum covering more recent developments in 1996.
:spark A pattern that dies. The term is typically used to describe a collection of cells periodically thrown off by an oscillator or spaceship, but other dying patterns, particulary those consisting or only one or two cells (such as produced by certain glider collisions, for example), are also described as sparks. For examples of small sparks see unix and HWSS. For an example of a much larger spark see Schick engine.
OO....OO O.O..O.O ..O..O.. O.O..O.O OO....OO
:sparker An oscillator or spaceship that produces sparks. These can be used to perturb other patterns without being themselves affected.
:sparky A certain c/4 tagalong, shown here attached to the back of a spaceship.
..........O.................... ..........O...............OO... ......OO.O.OOO..........OO...O. O.OO.OO.OO..O.O...OO.OOOO...... O...OO..O.OO..OOO..O.OO..OO...O O.OO....OOO.O.OOO......OO..O... ........OO.O...............O..O O.OO....OOO.O.OOO......OO..O... O...OO..O.OO..OOO..O.OO..OO...O O.OO.OO.OO..O.O...OO.OOOO...... ......OO.O.OOO..........OO...O. ..........O...............OO... ..........O....................
:sparse Life This refers to the study of the evolution of a Life universe which starts off as a random soup of extremely low density. Such a universe is dominated at an early stage by blocks and blinkers (often referred to collectively as blonks) in a ratio of about 2:1. Much later it will be dominated by simple infinite growth patterns (presumably mostly switch engines. The long term fate of a sparse Life universe is less certain. It may possibly become dominated by self-reproducing patterns (see universal constructor/destructor), but it is not at all clear that there is any mechanism for these to dealt with the all junk produced by switch engines.
:speed of light A speed of one cell per generation, the greatest speed at which any effect can propagate.
:S-pentomino Conway's name for the following pentomino.
..OO OOO.
:spider (c/5 orthogonally, p5) This is the smallest known c/5 spaceship. It was found by David Bell in April 1997. Its side sparks have proved very useful in constructing c/5 puffers, including rakes.
......O...OOO.....OOO...O...... ...OO.OOOOO.OO...OO.OOOOO.OO... .O.OO.O.....O.O.O.O.....O.OO.O. O...O.O...OOOOO.OOOOO...O.O...O ....OOO.....OO...OO.....OOO.... .O..O.OOO.............OOO.O..O. ...O.......................O...
:spiral (p1)
OO....O .O..OOO .O.O... ..O.O.. ...O.O. OOO..O. O....OO
:squirter = pipsquirter
:S-spiral = big S
:stable A pattern is said to be stable if it is a parent of itself. See still life.
:stable glider reflector A stable reflector that reflects gliders.
:stable reflector Any stable pattern that can reflect gliders (or perhaps some other type of spaceship) without suffering permanent damage. Oscillating reflectors were known from early on (see relay and buckaroo for two examples), but it was not until October 1996 that the first example of a stable reflector was found, by Paul Callahan. All known stable reflectors take a long time to recover from a hit. Callahan's original reflector is not ready for another glider until 894 generations after the last one. In November 1996 Dean Hickerson found a variant in which this figure is reduced to 747. Dave Buckingham reduced this 672 in May 1997 using a somewhat different method, and in October 1997 Stephen Silver reduced it to 623 by a method closer to the original. Dieter Leithner has offered a $100 prize for the first person to construct a stable glider reflector (either 90 or 180 degrees) that fits in a 50x50 square. The best attempt so far is still too large to show in this lexicon.
:stairstep hexomino (stabilizes at time 63) The following predecessor of the blockade.
..OO .OO. OO..
:standard spaceship A glider, LWSS, MWSS or HWSS.
:star (p3)
.....O..... ....OOO.... ..OOO.OOO.. ..O.....O.. .OO.....OO. OO.......OO .OO.....OO. ..O.....O.. ..OOO.OOO.. ....OOO.... .....O.....
:stator The cells of an oscillator that are always on. Compare rotor. (The stator is sometimes taken to include also some of those cells which are always off.) The stator is divided into the bushing and the casing.
:step Another term for a generation. This term is mainly used in describing conduits. For example, a 64-step conduit is one through which the active object takes 64 generations to pass.
:still life Any stable pattern. For the purposes of enumerating still lifes this definition is, however, unsatisfactory because, for example, any pair of blocks would count as a still life, and there would therefore be an infinite number of 8-bit still lifes. For this reason a stricter definition is often used, counting a stable pattern as a single still life only if its islands cannot be divided into two nonempty sets both of which are stable in their own right. Compare pseudo still life. Still lifes have been enumerated by Conway (4-7 bits), Robert Wainwright (8-10 bits), Dave Buckingham (11-13 bits), Peter Raynham (14 bits) and Mark Niemiec (15-24 bits). The resulting figures are shown below.
4 2 5 1 6 5 7 4 8 9 9 10 10 25 11 46 12 121 13 240 14 619 15 1353 16 3286 17 7773 18 19044 19 45759 20 112243 21 273188 22 672172 23 1646147 24 4051711
:stretcher Any pattern that grows by stretching a wick or agar. See boatstretcher and spacefiller.
:super beehive = honeycomb
:superfountain (p4) This sparker was found by Noam Elkies in February 1998. The resulting spark is more isolated than in Dean Hickerson's fountain.
...............OO......OO......OO..OO..OO..... .........OO.....O......O.....O..O..O..O..O.... ....O....O.O.OOO....OO.O.....OO.....OOO.O.O... ...O.O.....O.O.....O..O........OOOOO....O..O.. ....O.....O..O....O.O......OOOO..O...OO..O.O.. ....O.......OOOO..O.OO....O....OOOOO...O.O..OO ....OOO...O.....O.O..O....OO..O...O..OO.O.O.O. ........OO..O.OO.O.OO....OO..O....O......OO.O. ....O...O......O.O...OO.OO...OOOO....OO.O..O.. ...O.....O.O.....O...O.O.OOOOO.O......O.OOO... ....O...OOO.....O....O..........OOO..O........ ....OOO.OO..OO..O..OOOO..O.O.OO.O.O..O.OO..... O...O.........O...OO.OO.O..O......O..O..O..... ....OOO.OO..OO..O..O...OOO......OO....OO...... ....O...OOO.....O...O...O..................... ...O.....O.O.....O.....O...O.................. ....O...O......O.O..OOO...OO.................. ........OO..O.OO.O.O...OO..................... ....OOO...O.....O..O.O...OOO.................. ....O.......OOOO...O.OOOO..O.................. ....O.....O..O......O.....O................... ...O.O.....O.O.......OOOOO.................... ....O....O.O.OOO.......O...................... .........OO.....O............................. ...............OO.............................
:superstring An orthogonal row of cells, in principle infinite, stabilized on one side so that it moves at the speed of light, usually leaving debris behind. The row can often be made finite by providing two tracks between which the superstring runs. This gives a fuse which can be made as wide as desired. The following example is by Tony Smithurst.
.OO.......................................................... O..O...O...O...O...O...O...O...O...O...O...O...O...O...O...O. ....O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O O..O...O...O...O...O...O...O...O...O...O...O...O...O...O...O. .OOO......................................................... ..OO......................................................... ..OO......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ..OO......................................................... ..OO......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ..OO......................................................... ..OO......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ..OO......................................................... ..OO......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ..OO......................................................... ..OO......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ...O......................................................... ..OO......................................................... ..OO......................................................... .OOO......................................................... O..O...O...O...O...O...O...O...O...O...O...O...O...O...O...O. ....O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O.O O..O...O...O...O...O...O...O...O...O...O...O...O...O...O...O. .OO..........................................................
:swan (c/4 diagonally, p4) A diagonal spaceship producing some useful sparks (see boatstretcher for one simple use). Found by Tim Coe in February 1996.
.O..........OO.......... OOOOO......OO........... O..OO........O.......OO. ..OO.O.....OO......OOO.O ...........OO...O.OO.... .....O.O......OO........ ..........OOO.O....O.... .......OOO...O....O..... ........O.......O....... ........O......O........ ........................ ...........O............
:switch engine The following pattern, which in itself is unstable, but which can be used to make c/12 diagonal puffers and spaceships. The switch engine was discovered by Charles Corderman in 1971. Stabilized switch engines are the most natural puffers in Life, being the only ones ever seen to occur from random starting patterns. There are two basic types, a p288 block-laying type (the more common of the two) and p384 glider-producing type. Patterns giving rise to the former type can be seen under infinite growth, and one giving rise to the latter type is shown under time bomb. See also Noah's ark and Cordership.
.O.O.. O..... .O..O. ...OOO
:synthesis = glider synthesis
:T = T-tetromino
:table The following induction coil.
OOOO O..O
O..O OOOO .... OOOO O..O
:tagalong An object which is not a spaceship in its own right, but which can be attached to one or more spaceships to form a larger spaceship. For examples see fly, pushalong, sidecar and sparky. See also Schick engine, which consists of a tagalong attached to two LWSS (or similar).
:tail spark A spark at the back of a spaceship. For example, the 1-bit spark at the back of a LWSS, MWSS or HWSS in their less dense phases.
:teardrop (p1) The following fairly common formation of two beehives.
.O....... O.O...... O.O...... .O....... ......... ......... ......OO. .....O..O ......OO.
:technician (p5) Found by Dave Buckingham.
.....O..... ....O.O.... ....OO..... ..OO....... .O...OOO... O..OO...O.O .OO....O.OO ...O.O.O... ...O...O... ....OOO.... ......O.O.. .......OO..
:technician finished product = technician
:ternary reaction Any reaction between three objects. In particular, a reaction in which two gliders from one stream and one glider from a crossing stream of the same period annihilate each other. This can be used to combine two glider guns of the same period to produce a new glider gun with double the period.
OO....OO O.O..O.O ..O..O.. ..O..O.. ...OO...
:tetraplet Any 4-cell polyplet.
:tetromino Any 4-cell polyomino. There are five such objects, shown below. The first is the block, the second is the T-tetromino and the remaining three rapidly evolve into beehives.
OO......OOO......OOOO......OOO......OO. OO.......O...................O.......OO
:The Recursive Universe A popular science book by William Poundstone (1986) dealing with the nature of the universe, illuminated by parallels with the game of Life. This book brought to a wider audience many of the results that first appeared in LifeLine. It also outlines the proof of the existence of a universal constructor/destructor in Life first given in Winning Ways.
:thunderbird (stabilizes at time 243)
OOO ... .O. .O. .O.
:tick = generation
:time bomb The following pattern by Doug Petrie, which is really just a stabilized glider-producing switch engine in disguise. See infinite growth for some better examples of a similar nature.
.O...........OO O.O....O......O .......O....O.. ..O..O...O..O.. ..OO......O.... ...O...........
:TL = traffic light
:T-nosed p4 (p4) Found by Robert Wainwright.
.....O..... .....O..... ....OOO.... ........... ........... ........... ...OOOOO... ..O.OOO.O.. ..O.O.O.O.. .OO.O.O.OO. O..OO.OO..O OO.......OO
:toad (p2) Found by Simon Norton, this is the second most common oscillator.
.OOO OOO.
:toadsucker A hassler that hassles a toad, particularly in the manner of shown in the following example. Two domino sparkers, here pentadecathlons, apply their sparks to the toad in order to move it. The remarkable thing is that the sparks when applied again move the toad back to where it came from. The period of the toadsucker is two or four times that of the domino sparker, depending on whether the period of the domino sparker is even or odd. In the example below the period is therefore 60.
.O................ .O..............O. O.O.............O. .O.............O.O .O......O.......O. .O......OO......O. .O......OO......O. O.O......O......O. .O.............O.O .O..............O. ................O.
:toaster (p5) Found by Dean Hickerson.
....O......OO.. ...O.O.OO..O... ...O.O.O.O.O... ..OO.O...O.OO.. O...OO.O.OO...O ...O.......O... ...O.......O... O...OO.O.OO...O ..OO.O...O.OO.. ...O.O.O.O.O... ...O.O.OO..O... ....O......OO..
:total aperiodic Any finite pattern such that every cell in the Life plane is eventually aperiodic. The first example was found by Bill Gosper in November 1997. A few days later he found the following much smaller example consisting of three copies of a p12 backrake by Dave Buckingham.
...............O........................................ .OO...........O......................................... .OOO..........O......................................... .OOO..........O..O...................................... O.OO..........OOO....................................... OOO..................................................... .O...................................................... ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ...OO................................................... ...OOO.................................................. ..O.OO.................................................. ..OOO................................................... ...O............OO...................................... ...............OOO...................................... ...............OOO...................................... ...............OO.O..................................... ...O....OO.O....OOO..................................... ..O.....O..O.....O...................................... ..O......OOO............................................ ..O..O.................................................. ..OOO................................................... ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ..........OO.............O.............................. .........OOO............O............................... .........OO.O...........O............................... ..........OOO...........O.......OOO..................... ...........O............O..O...OOOOO.................... ........................OOO....OOO.OO.......OO........O. ..................................OO.......OOOO........O ...........................................OO.OO...O...O .............................................OO.....OOOO ........................................................ ........................................................ ........................................................ .......................O..........................OO.... ......................O..........................OO.OO.. ......................O...........................O..O.. ......................O..O........................O..O.. .........O............OOO..........................OO... ..........O......................O...................... ..........O.......................O..................... ..........O...................O...O..................... .......O..O....................OOOO...............OO.... ........OOO....O.OO...OO.......................OOO.OO... ...............OOO...OOO.......................OOOOO.... ................O....OO.O.......................OOO..... ......................OOO............................... .......................O................................
:T-pentomino Conway's name for the following pentomino.
OOO .O. .O.
:track A path made out of conduits, often ending where it begins so that the active object is cycled forever, forming an oscillator or a gun.
.....................OO....OO................... .....................O.O..O.O................... .......................O..O..................... ......................OO..OO.................... .....................OOO..OOO................... .......................O..O..................... ...............................O................ ..............................O.OO.............. ..................................O............. ..........................O...O..O.O............ ..........................O.....O..O............ ..........................O......OO............. .........OO..................................... ........O..O..........OOO...OOO................. .......O.O.O.................................... ......OOO.O...............O..................... ......OOO.................O..................... ..........................O..................... ............OOO................................. OO..O................OOO........................ O..OO.....O.....O............................... .OOOOO....O.....O..O.....O.................O..OO ..........O.....O..O.....O.................OO..O ...................O.....O.......OOO......OOOOO. .OOOOO......OOO................................. O..OO................OOO.......O.....O.......... OO..O..........................O.....O....OOOOO. ...............................O.....O.....OO..O ...........................................O..OO .................................OOO............ .......................................OO....... ......................................OOO....... .....................................O.OO....... ....................................O.O......... ....................OOO.............O..O........ .....................................OO......... .............OO....O..O......................... ............O..O................................ ............O.O.O............................... .............O..O............................... .................O.............................. ..............O.O............................... .....................O..O....................... ...................OOO..OOO..................... ....................OO..OO...................... .....................O..O....................... ...................O.O..O.O..................... ...................OO....OO.....................
:traffic jam Any traffic light hassler, such as traffic circle. The term is also applied to the following reaction, used in many traffic light hasslers, in which two traffic lights interact in such a way as to reappear after 25 generations with an extra 6 spaces between them.
..OOO........... ...........OOO.. O.....O......... O.....O..O.....O O.....O..O.....O .........O.....O ..OOO........... ...........OOO..
:traffic light (p2) A common formation of four blinkers.
..OOO.. ....... O.....O O.....O O.....O ....... ..OOO..
:trans-beacon on table (p2)
....OO .....O ..O... ..OO.. ...... OOOO.. O..O..
OO... O.O.. .O.O. ...O. ...OO
:trans-loaf with tail (p1)
.O.... O.O... O..O.. .OO.O. ....O. ....OO
:transparent block reaction A certain reaction between a block and a Herschel predecessor in which the block reappears in its original place some time later. This reaction, found by Dave Buckingham in 1988, in effect completely transforms the Herschel without affecting the block. It has been used in some Herschel conduits, and in the gunstars. Because the reaction involves a Herschel predecessor rather than an actual Herschel, the following diagram shows instead a B-heptomino (which evolves into a block and a Herschel).
O............. OO..........OO .OO.........OO OO............
:transparent debris effect = transparent block reaction
:trice tongs (p3) Found by Robert Wainwright.
OO..... OO..O.. ..OO.O. ..O..O. .O...OO ..OOO.. ....O..
:triomino Either of the two 3-cell polyominoes. The term is rarely used in Life, since the two objects in question are simply the blinker and the pre-block.
:triplet Any 3-cell polyplet. There are 5 such objects, shown below. The first two are the two triominoes, and the other three vanish in two generations.
O..................O.......O.......O.. OO......OOO......OO.......O.O.......O. .....................................O
:tripole (p2) The barberpole of length 3.
OO.... O.O... ...... ..O.O. .....O ....OO
:true Opposite of pseudo. A gun emitting a period n stream of spaceships (or rakes) is said to be a true period n gun if its mechanism oscillates with period n. True period n guns are known to exist for all periods greater than 61 (see My Experience with B-heptominos in Oscillators), but only a few smaller periods have been achieved, namely 24, 30, 44, 46, 48, 50, 54, 56 and 60. (Credits for these small period guns are: p30, p46 and p60 by Bill Gosper in 1970-1971, p44 by Dave Buckingham in 1992, p50 by Dean Hickerson in 1996, p24 and p48 by Noam Elkies in 1997 and p54 and p56 by Dieter Leithner in 1998.)
:T-tetromino The following predecessor of a traffic light.
OOO .O.
.O. O.O .O.
:tubstretcher See boatstretcher.
:tub test tube baby (p2) See test tube baby.
.O......O. O.O....O.O .O.O..O.O. ...O..O... ...O..O... ....OO....
:tub with tail (p1)
.O... O.O.. .O.O. ...O. ...OO
:tubber (p3)
....O.O...... ....OO.O..... .......OOO... ....OO....O.. OO.O..OO..O.. .O.O....O.OO. O...O...O...O .OO.O....O.O. ..O..OO..O.OO ..O....OO.... ...OOO....... .....O.OO.... ......O.O....
:tugalong = tagalong
:tumbler (p14) The smallest known p14 oscillator. Found by George Collins.
.O.....O. O.O...O.O O..O.O..O ..O...O.. ..OO.OO..
:turtle (c/3 orthogonally, p3) Found by Dean Hickerson.
.OOO.......O .OO..O.OO.OO ...OOO....O. .O..O.O...O. O....O....O. O....O....O. .O..O.O...O. ...OOO....O. .OO..O.OO.OO .OOO.......O
:twin peaks = twinhat
:twin bees shuttle (p46) Found by Bill Gosper, this is used in all known true p46 guns. See new gun for an example. There are various ways to stabilize the ends, two of which are shown in the diagram. On the left is David Bell's double block reaction (which results in a shorter, but wider, shuttle than usual), and on the right is the stabilization by a single block. This latter method produces a very large spark which is useful in a number of ways. Adding a symmetrically placed block below this one suppresses the spark. See also p54 shuttle.
.OO........................ .OO........................ ........................... ...............O........... OO.............OO........OO OO..............OO.......OO ...........OO..OO.......... ........................... ........................... ........................... ...........OO..OO.......... OO..............OO......... OO.............OO.......... ...............O........... ........................... .OO........................ .OO........................
..O...O.. .O.O.O.O. .O.O.O.O. OO.O.O.OO ....O....
:twirling T-tetsons II (p60) Found by Robert Wainwright. This is a pre-pulsar hassled by toads.
.......OO...OO.......... ......O.......O......... .........O.O............ .......OO...OO.......... ........................ ........................ ........................ .....................OOO ....................OOO. .............O.......... OOO.........OOO......... .OOO.................... ....................OOO. .....................OOO ........................ .OOO.................... OOO.........OOO......... .............O.......... ........................ ........................ ..........OO...OO....... ............O.O......... .........O.......O...... ..........OO...OO.......
OO....... .O....... .O.O..... ..OO..... .....OO.. .....O.O. .......O. .......OO
:two pulsar quadrants (p3) Compare pulsar quadrant.
....O.... ....O.... ...OO.... ..O...... O..O..OOO O...O.O.. O....O... ......... ..OOO....
:underpopulation Death of cell caused by it having fewer than two neighbours.
:unit Life cell A rectangular pattern, of size greater than 1x1, that can simulate Life in the following sense. The pattern by itself represents a dead Life cell, and some other pattern represents a live Life cell. When the plane is tiled by these two patterns (which then represent the state of a whole Life universe) they evolve, after a fixed amount of time, into another tiling of the plane by the same two patterns which correctly represents the Life generation following the one they initially represented. It is usual to use capital letters for the simulated things, so, for example, for the first known unit Life cell (constructed by David Bell in January 1996), one Generation is 5760 generations, and one Cell is 500x500 cells.
:universal computer A computer that can compute anything that is computable. (The concept of computability can be defined in terms of Turing machines, or by Church's lambda calculus, or by a number of other methods, all of which can be shown to lead to equivalent definitions.) The relevance of this to Life is that both Bill Gosper and John Conway proved early on that it is possible to construct a universal computer in the Life universe. (The construction has never been carried out, because, even with the improvements that have since been devised, it would be enormous.) Conway's proof is outlined in Winning Ways, and also in The Recursive Universe. See also sliding block memory and universal constructor/destructor.
:universal constructor/destructor A pattern that is capable of constructing any pattern that has a glider synthesis, and of deleting any pattern that can be deleted by gliders. An outline of Conway's proof that such a pattern exists can be found in Winning Ways, and also in The Recursive Universe. The key mechanism for the production of gliders with any given path and timing is known as side-tracking, and is based on the kickback reaction. A universal constructor/destructor is most useful when attached to a universal computer, which can be programmed to control the constructor to produce the desired pattern of gliders. In what follows we will assume that a universal constructor/destructor always includes this computer. The existence of a universal constructor/destructor, itself both constructible and deletable by gliders, has a number of theoretical consequences. Firstly, if such a constructor has an n-glider synthesis (including 2 gliders used to form the block which encodes the program for the universal computer) then any pattern with a glider synthesis must also have an n-glider synthesis, for we could arrange for the program to specify that the constructor make this pattern and delete itself. Alternatively, the constructor could be programmed to make copies of itself. This is a replicator. The constructor could even be programmed to make just one copy of itself translated by a certain amount and then delete itself. This would be a (very large and very slow) spaceship. Any translation is possible (except that it must not be too small), so that the spaceship could travel in any direction. It could also travel slower than any given speed, since we could program it to perform some time-wasting task (such as repeatedly constructing and deleting a block) before copying itself. Of course, we could also choose for it to leave some debris behind, thus making a puffer. It is also possible to show that the existence of a universal constructor implies the existence of a stable reflector. This proof is not so easy, however, and is no longer of much significance now that explicit examples of stable reflectors have been constructed.
:unix (p6) Two blocks trying to eat a long barge. This is a useful sparker, found by Dave Buckingham.
.OO..... .OO..... ........ .O...... O.O..... O..O..OO ....O.OO ..OO....
:up boat with tail = trans-boat with tail
:U-pentomino Conway's name for the following pentomino.
O.O OOO
.O.... O.O... .O.O.. ..O.O. ...O.O ....O.
.O... O.O.. .O.O. ..O.O ...OO
.....OO ......O .....O. ....O.. ...O... O.O.... OO.....
:very long house The following induction coil.
.OOOOO. O..O..O OO...OO
OO... O.O.. .O.O. ..O.O ...OO
OO.... O.O... ...O.O ....OO
:volcano Any of a number of p5 oscillators which produce sparks. See lightweight volcano, middleweight volcano and heavyweight volcano.
:V-pentomino Conway's name for the following pentomino.
O.. O.. OOO
:washerwoman (2c/3 p18 fuse) A fuse by Earl Abbe.
O....................................................... OO....O.....O.....O.....O.....O.....O.....O.....O.....O. OOO..O.O...O.O...O.O...O.O...O.O...O.O...O.O...O.O...O.O OO....O.....O.....O.....O.....O.....O.....O.....O.....O. O.......................................................
:washing machine (p2)
.OO.OO. O.OO..O OO....O .O...O. O....OO O..OO.O .OO.OO.
:weld To join two or more still lifes or oscillators together. This is often done in order to fit the objects into a smaller space than would otherwise be possible. The simplest useful example is probably the integral sign, which can be considered as a pair of welded fishhooks.
:Wheels, Life, and other Mathematical Amusements One of Martin Gardner's books (1983) that collects together material from his column in Scientific American. The last three chapters of this book contain all the Life stuff.
:wick A stable or oscillating linearly repeating pattern that can be made to burn at one end. See fuse.
:wickstretcher A spaceship-like object which stretches a wick that is fixed at the other end. The wick here is assumed to be in some sense connected, otherwise most puffers would qualify as wickstretchers. The first example of a wickstretcher was found in October 1992 (front end by Hartmut Holzwart and back end by Dean Hickerson) and stretches ants at a speed of c/4. This is shown below with an improved back end (also by Hickerson). For another example see boatstretcher.
.................OO.............................. .............OO....O............................. ............OOO.O................................ O.OO..OO...O...OOOO.O.O....OO.......OO........... O....OO..O........O.OOO....O....OO.O..O.OO.O..... O.OO....OO.OO....O...........O...O.O.OO.O.OO..... ......O.......O.............OO.....O..O.O...OO... .....O.........O.O....OOO...O....O..O.O.OOO...O.. .....O.........O.O....OOO.OO.O..OO.O.O...O..OO.O. ......O.......O.............OO.O...OO....OO....O. O.OO....OO.OO....O..........O........OO.O.O.OO.OO O....OO..O........O.OOO........O...O...OO.O..O.O. O.OO..OO...O...OOOO.O.O.......O.O...OO....O..O.O. ............OOO.O..............O.....O.OOO....O.. .............OO....O.................O.O......... .................OO...................O..........
:wicktrailer Any extensible tagalong.
:wing The following induction coil. This is generation 2 of block and glider.
.OO. O..O .O.O ..OO
:Winning Ways A two-volume book (1982) by Elwyn Berlekamp, John Conway and Richard Guy on mathematical games. The last chapter of the second volume concerns Life, and outlines a proof of the existence of a universal constructor/destructor.
:worker bee (p9) Found by Dave Buckingham.
OO............OO .O............O. .O.O........O.O. ..OO........OO.. ................ .....OOOOOO..... ................ ..OO........OO.. .O.O........O.O. .O............O. OO............OO
:W-pentomino Conway's name for the following pentomino.
O.. OO. .OO
:Xlife A popular freeware Life program that runs under the X Window System. The original code was written by Jon Bennett.
:X-pentomino Conway's name for the following pentomino.
.O. OOO .O.
:Y-pentomino Conway's name for the following pentomino.
..O. OOOO
:Z-hexomino The following hexomino. See pentoad.
OO. .O. .O. .OO
:Z-pentomino Conway's name for the following pentomino.
OO. .O. .OO