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Life Lexicon
Release 10, 1998 November 8th |
This lexicon was compiled by Stephen A. Silver - see below for additional credits. I can be contacted at sasilver@hotmail.com.
Other sources include the works listed in the bibliography at the end of this lexicon, as well as 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, Robert Wainwright and Heinrich Koenig.
Most of the information on recent results is from the discoverers themselves.
Dean Hickerson, David Bell, Peter Rott and especially Dieter Leithner and Alan Hensel provided 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. (If you use Johan Bontes' Life32 then you can, of course, paste the pattern directly into the Life program.) I have restricted myself to diagrams of size 64×64 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 positive integer), 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.
There are certainly omissions, particularly in names of discoverers and dates of discovery. Any information to fill these gaps 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 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) Found by Dean Hickerson in March 1993.
....OO.... ...O..O... ...OOOO... .O.O..O.O. O........O O........O .O.O..O.O. ...OOOO... ...O..O... ....OO....
:agar Any pattern covering the whole plane that is periodic in both space and time. The simplest (nonempty) agar is the stable one extended by the known spacefillers. For some more examples see chicken wire, onion rings and Venetian blinds. Tiling the plane with the pattern O......O produces another interesting example: a p6 agar which has a phase of density 3/4, which is the highest yet obtained for any phase of an oscillating pattern.
:aircraft carrier (p1) This is the smallest still life that has more than one island.
OO.. O..O ..OO
:airforce (p7) Found by Dave Buckingham.
.......O...... ......O.O..... .......O...... .............. .....OOOOO.... ....O.....O.OO ...O.OO...O.OO ...O.O..O.O... OO.O...OO.O... OO.O.....O.... ....OOOOO..... .............. ......O....... .....O.O...... ......O.......
:AK47 reaction The following reaction (found by Rich Schroeppel and Dave Buckingham) 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 very small (but pseudo) p94 glider gun found by Paul Callahan in July 1994, and was in 1990 the basis for the Dean Hickerson's construction of the first true p94 gun. (This latter gun was enormous, and has now been superceded by comparatively small Herschel loop guns.)
.....O.... ....O.O... ...O...O.. ...O...O.. ...O...O.. ....O.O... .....O.... .......... ..OO...... ...O...... OOO.....OO O.......OO
:Al Jolson (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 perpendicular 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. Experiments show that for random soups with moderate initial densities (say 0.25 to 0.5) the resulting ash has a density of about 0.0287. (This is, of course, based on what happens in finite fields. In infinite fields the situation may conceivably be different in the long run because of the effect of certain initially very rare objects such as replicators.)
: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 backwards rake. For an example see total aperiodic.
: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.
:basic shuttle = queen bee shuttle
: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) 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. A bi-loaf can be half a bakery:
.O..... O.O.... O..O... .OO.O.. ...O.O. ...O..O ....OO.or it can be the following much less common still life:
..O.... .O.O... O..O... .OO.OO. ...O..O ...O.O. ....O..or the following pure glider generator:
..O. .O.O O..O .OO. O..O O.O. .O..
:bipole (p2) The barberpole of length 2.
OO... O.O.. ..... ..O.O ...OO
.OO.... O..O... O..O... .OO.OO. ...O..O ...O..O ....OO.
:bi-ship = ship-tie
:Black&White = Immigration
:blasting cap A name used at MIT for generation 1 of the pi-heptomino. Still occasionally used today.
: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.
..........OOOO............. ..........O...O............ ..........O................ .OO........O..O............ OO.OO...................... .OOOO...O.................. ..OO...O.OO........O....OOO ......O...O........O....O.O ..OO...O.OO........O....OOO .OOOO...O.................. OO.OO...................... .OO........O..O............ ..........O................ ..........O...O............ ..........OOOO.............
:biting off more than they can chew = eater-bound pond
:blasting cap Generation 1 of the pi-heptomino. A term used at MIT and still occasionally encountered.
: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. See also filter.
......O.O. .....O.... OO..O....O OO.O..O.OO ....OO....
:block on big table = block and dock
:block on table (p1)
..OO ..OO .... OOOO O..O
: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. 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 the switched back to 0 again. The first crossing glider will survive, but the second will be destroyed. (In January 1997 David Bell found a method of reading the bit while setting it to 0. A MWSS is fired at the boat-bit. If it is already 0 then the MWSS passes unharmed, but if it is 1 then the boat and the MWSS are destroyed and, with the help of a fishhook, converted into a glider which travels back along the exact same path that is used by the gliders that toggle the boat-bit.)
......O.................. .......O................. .....OOO................. ......................... ......................... ......................... ......................... ......................... ......................... ......................... ................O........ ..............O.O........ ..........OO...OO........ ...........OO............ ..........O..........O.OO .....................OO.O ......................... ......................... ......................... ......................... ......................... .O....................... .OO...................... O.O......................
................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 tie 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.....
:bounding box The smallest rectangular array of cells that contains the whole of a given pattern. For oscillators and guns this usually is meant to include all phases of the pattern, but excludes, in the case of guns, the outgoing stream(s).
:bow tie = boat-tie
:brain (c/3 orthogonally, p3) Found by David Bell.
.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 M=moving and S=still). 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 mosquito4.
:bridge A term used in naming certain still lifes (and the stator part of certain oscillators). It indicates that the object consists of two smaller objects joined edge to edge, as in snake bridge snake.
: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. This was found by Dave Buckingham. The name is due to Bill Gosper.
..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 parent 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 The following pattern, or the formation of two beehives that it evolves into after 33 generations. (Compare teardrop, where the beehives are five cells closer together.)
O... OO.. O.O. .OOO
: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 slower receding spaceship.
:Cambridge pulsar CP 48-56-72 = pulsar (The numbers refer to the populations of the three phases. The Life pulsar was indeed discovered at Cambridge, like the first real pulsar a few years earlier.)
: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. In terms of its minimum cell count of 12 this is the smallest p3 oscillator.
..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.
It is common for the neighbourhood of a cell to be the 3×...×3 (hyper)cube centred on that cell. (This includes those cases where the neighbourhood might more naturally be thought of as a 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, a less common variant of the B-heptomino.
.OOO OOO. .O..
:Cheshire cat A block predecessor by C. R. Tompkins that unaccountably appeared both in Scientific American and in Winning Ways. See also grin.
.O..O. .OOOO. O....O O.OO.O O....O .OOOO.
:chicken wire A type of stable agar of density 1/2. The simplist version is formed from the tile:
OO.. ..OOBut the "wires" can have length greater than two and need not all be the same. For example:
OO...OOOO..... ..OOO....OOOOO
:cigar = mango
:cis-beacon on anvil (p2)
...OO. ....O. .O.... .OO... ...... .OOOO. O....O .OOO.O ...O.OO
:cis-beacon on table (p2)
..OO ...O O... OO.. .... OOOO O..O
.O... O.O.. OO.O. ...O. ...OO
:cis fuse with two tails (p1) See also pulsar quadrant.
...O.. .OOO.. O...OO .O..O. ..O.O. ...O..
.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 the term has also been used in other senses, often imprecise.
: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
:colorized Life A cellular automaton which is the same as Life except for the use of a number of different ON states ("colours"). All ON states behave the same for the purpose of applying the Life rule, but additional rules are used to specify the colour of the resulting ON cells. Examples are Immigration and QuadLife.
:compression = repeat time
: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
:converter A conduit in which the input object is not of the same type as the output object. This term tends to be preferred when either the input object or the output object is a spaceship.
The following diagram shows a p8 pi-heptomino-to-HWSS converter. This was originally found by Dave Buckingham in a larger form (using a figure-8 instead of the boat). The improvement shown here is by Bill Gosper (August 1996). Dieter Leithner has since found (much larger) oscillators of other periods to replace the Kok's galaxy.
.O.O..O........ .OOO.O.OO...... O......O.....O. .O.....OO...O.O .............OO OO.....O....... .O......O...... OO.O.OOO....... ..O..O.O....... ............OOO ............O.O ............O.O
: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 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). Hickerson's original Cordership used 13 switch engines. He soon reduced this to 10, and in August 1993 to 7. In July 1998 he reduced it to just 6, and this is shown below.
.............................OOO................................ ............................O...O............................... ............................O...O............................... ............................O...O............OOO................ .............................................OOO................ .............................OO.OO.........OO....O.............. ..............................O..O.........OOO.O.O.............. ...............................O.O..........OO...O.............. ................................OO..........OOOOO............... .............................O...O............O.......OO........ ............................O.O.O.O...................OO........ .............................O.................................. ................................................................ ................................................................ ..................OO.....................O.O.................... .....................OO....O................O................... ..................OO.OOOO...O...........O...O................... ...............OOOOO....OOOO............O...O.................OO ..................OOO......O............O..O..................OO ...................O.....................O...................... ..................OOO........................................... .........................O............OO........................ .........................O............OO........................ ................................................................ O.O.................................................O.O......... OOO............................O....................OOO......... OO...............O............O.O...................OO.......... .................O............O.O............................... .................O.............O................................ ...O...................................................O........ .O.O...............O.................................O.O........ .OOO..............O.O................................OOO........ ....O..............O....................................O....... OOOOO...............................................OOOOO....... ................................................................ ................................................................ ........................................OOO......O.............. .........................................OO...OO.O.............. ........................................OO.....O.O.............. .............................................OOO.O.............. ................................................OO.............. ................................................................ ................................................................ ................................................................ .....OO......................................................... .....OO......................................................... ................................................................ ................................................................ ........................O.O..................................... ........................OOO..................................... ........................OO...................................... ................................................................ .............OO................................................. .............OO............O.................................... .........................O.O.................................... .........................OOO.................................... ............................O................................... ........................OOOOO................................... ................................................................ ................................................................ .....................OO......................................... .....................OO.........................................
: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 a caterer, a jam, a HW emulator and a T-tetromino. The jam can be moved down a space and/or replaced by another caterer.
.....OO....OO....OO.... ....O..O.O....O.O..O... ....OOO..........OOO... .......OO......OO...... ......O..OOOOOO..O..... ......OO........OO..... .OO.................... O..O................... O.O..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.
:dead spark coil (p1) Compare spark coil.
OO...OO O.O.O.O ..O.O.. O.O.O.O OO...OO
:density The density of a pattern is the limit of the proportion of live cells in a (2n+1)×(2n+1) square centred on a particular cell as n tends to infinity, when this limit exists. (Note that it does not make any difference what cell is chosen as the centre cell. Also note that if the pattern is finite then the density is zero.)
The question of what the maximum density of a stable pattern is remained open for about quarter of a century until Noam Elkies proved that it is 1/2, which had been the conjectured value. (This value is easily attained. The problem was to prove that no higher density is possible.) A corollary is that a still life with an m × n bounding box has at most (m+1)(n+1)/2 cells.
But what is the maximum average density of an oscillating pattern? The answer is conjectured to be 1/2 again, but this remains unproved - the best upper bound so far obtained is 8/13.
The maximum possible density for a phase of an oscillating pattern is also unknown. An example with a density of 3/4 is known (see agar), but densities arbitrarily close to 1 may perhaps be possible.
:D-heptomino = Herschel
:diamond = tub
:diamond ring (p3) Found by Dave Buckingham in 1972.
......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 (noticed by Stephen Silver 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-barrelled Of a gun, emitting two streams of spaceships (or rakes). The following diagram shows a double-barrelled p104 glider gun found by Noam Elkies in March 1996.
.OO.................................... .OO.................O.................. ...................O.O............O.O.. ....................O............O..... OO.......OO.......................O..O. OO.O.....OO.......................O.O.O ...O.......................O.......O..O ...O.......................OO.......OO. O..O.................OO.....O.......... .OO..................O................. .....................OOO............... ....................................OO. ....................................OO. .OO.................................... O..O................................... O.O.O................O.O....OO.....OO.. .O..O.................OO....OO.....OO.O .....O............O...O...............O ..O.O............O.O..................O ..................O................O..O ....................................OO.
: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 interact with certain patterns without suffering any permanent damage. (If it doesn't suffer even temporary damage then it may be referred to as a rock.) The fishhook is a very common eater, and the term "eater" is often used specifically for this object. Other eaters include eater2, eater3, eater4 and even the humble block. Another useful eater is shown below, feasting on a glider.
...O..... ...O.O... ...OO.... ......... .......OO ...O...OO ..O.O.... .O.O..... .O....... OO.......
:eater1 = fishhook
:eater2 (p1) This eater was found by Dave Buckingham in the 1970s. Mostly it works like the ordinary eater (see fishhook) but with two slight differences that make it useful despite its size: it takes longer to recover from each bite and it acts like an eater in two directions. The first 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. An eater2 variant noticed by Stephen Silver in May 1998 that is useful for obtaining smaller bounding boxes can be seen under gliderless.
...O.OO .OOO.OO O...... .OOO.OO ...O.O. ...O.O. ....O..
:eater3 (p1) This large symmetric eater, found by Dave Buckingham, 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...
:eater4 (p1) Another eater by Dave Buckingham, which he found in 1971, but did not recognize as an eater until 1975 or 1976. It can't eat gliders, but it can be used for various other purposes. The four NE-most centre cells regrow in a few generations after being destroyed by taking a bite out of something.
...OO......... ...O.......... OO.O.......... O..OO......... .OO....O...... ...OOOOO...... ...O....OO.... ....OO..O..... ......O.O..... ......O.O.O..O .......OO.OOOO .........O.... .........O.O.. ..........OO..
: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 shooter A gun which fires its gliders (or whatever) right at the edge of the pattern, so that it can be used to fire them closely parallel to others. This is useful for constructing complex guns. Compare glider pusher, which can in fact be used for making edge shooters.
The following diagram shows a p46 edge shooter found by Paul Callahan in 1994.
OO............OO..O....OO..OO............. OO............O.OO......OO.OO............. ...............O......O.O................. ...............OOO....OO.................. .......................................... ...............OOO....OO.................. ...............O......O.O................. OO............O.OO......OO................ OO............OO..O....OO................. .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... ...............................OOO...OOO.. ..............................O...O.O...O. .............................O...OO.OO...O .............................O.OO.....OO.O ...............................O.......O.. .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... .......................................... ...............................OO.....OO.. ...............................OO.....OO..
: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"). All known Herschel loops of periods 57, 58, 59 and 61 are emus. See also Quetzal.
:emulator Any one of three p4 oscillators that produce sparks similar to those produced by LWSS, MWSS and HWSS. See LW emulator, MW emulator and HW emulator. Larger emulators are also 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 June 1980.
:Eureka (p30) A pre-pulsar shuttle found by Dave Buckingham and Robert Wainwright. A variant is obtained by shifting the top half two spaces to either side.
.O..............O. O.O....O.......O.O .O...OO.OO......O. .......O.......... .................. .................. .................. .......O.......... .O...OO.OO......O. O.O....O.......O.O .O..............O.
: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.
:extra extra long snake (p1)
OO...... O.O..... ...O.... ....O... .....O.O ......OO
:extra long snake (p1)
OO..... O.O.... ...O... ....O.O .....OO
: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).
:fanout A mechanism that emits two or more objects of some type for each one that it receives. Typically the objects are gliders or Herschels.
: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 early on.
OOO... OOO... OOO... ...OOO ...OOO ...OOO
:filter Any oscillator used to delete some but not all of the spaceships in a stream. An example is the blocker, which can be positioned so as to delete every other glider in a stream of period 8n+4, and can also do the same for LWSS streams. Other examples are the MW emulator and T-nosed p4 (either of which can be used to delete every other LWSS in a stream of period 4n+2), the fountain (which does the same for MWSS streams) and a number of others, such as the p6 pipsquirter, the pentadecathlon and the p72 oscillator shown under factory. An other example, a p4 oscillator deleting every other HWSS in a stream of period 4n+2, is shown below. (The p4 oscillator here was found, with a slightly larger stator, by Dean Hickerson in November 1994.)
..........OOOO............ ....OO...OOOOOO........... OOOO.OO..OOOO.OO.......... OOOOOO.......OO........... .OOOO..................... .......................... ................OO........ ..............O....O...... .......................... .............O.O..O.O..... ...........OOOO.OO.OOOO... ........O.O....O..O....O.O ........OO.OO.O....O.OO.OO ...........O.O......O.O... ........OO.O.O......O.O.OO ........OO.O..........O.OO ...........O.O.OOOO.O.O... ...........O.O......O.O... ..........OO.O.OOOO.O.OO.. ..........O..OOO..OOO..O.. ............O..OOOO..O.... ...........OO.O....O.OO... ...........O..O....O..O... ............O..O..O..O.... .............OO....OO.....
: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 in November 1994, and named by Bill Gosper. See also filter.
.........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 in 1989.
...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, many years before Life.) It was known from the start that there are Gardens of Eden in Life, because of a theorem by Edward Moore that guarantees their existence in a wide class of cellular automata. Explicit examples have since been constructed, the first by Roger Banks, et al. at MIT in 1971. 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-block cycle An infinite oscillator based on the following reaction (which is very similar to that of the rephaser). The oscillator consists of copies of this reaction displaced 2n spaces from one another (for some n>6) with blocks added between the copies in order to cause the reaction to occur again halfway through the period. The period of the resulting infinite oscillator is 8n-20. (Alternatively, in a cylindrical universe of width 2n - or a toroidal one of width 2n and sufficient height - the oscillator just consists of two gliders and two blocks.)
...OO... ...OO... ........ ........ ..O..O.. O.O..O.O .OO..OO.
: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 diagram shows Leithner's p44 MWSS gun which he discovered in April 1997 (shown with Stephen Silver's May 1998 improvement to the bounding box using a modified eater2). This is the smallest known gliderless gun, and also the smallest known MWSS gun. It is based on an important p44 oscillator discovered by Dave Buckingham in early 1992. (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...........................
:glider pusher An arrangement of a queen bee shuttle and a pentadecathlon that can push the path of a passing glider out by one half-diagonal space. This was found by Dieter Leithner in December 1993 and is shown below. It is useful for constructing complex guns where it may be necessary to produce a number of gliders travelling on close parallel paths. See also edge shooter.
.........OO.............. .........OO.............. ......................... ..........O.............. .........O.O............. .........O.O............. ..........O.............. ......................... ......................... .......OO.O.OO........... .......O.....O........... ........O...O............ .O.......OOO............. ..O...................... OOO...................... ......................... ......................... .................O....O.. ...............OO.OOOO.OO .................O....O..
:gliders by the dozen (stabilizes at time 184) In early references this is usually shown in a larger form whose generation 1 is generation 8 of the form shown here.
OO..O O...O O..OO
:glider synthesis Construction of an object by means of glider collisions. It is generally assumed that the gliders
Glider syntheses for all still lifes and known oscillators with at most 14 cells were found by Dave Buckingham.
Perhaps the most interesting glider syntheses are those of spaceships, because these can be used to create 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.
A 3-glider synthesis of a pentadecathlon is shown in the diagram below. This was found in April 1997 by Heinrich Koenig and came as a surprise, as it was widely assumed that anything using just three gliders would already be known.
......O... ......O.O. ......OO.. .......... OOO....... ..O....... .O.....OO. ........OO .......O..
:glider train A certain puffer that produces two rows of blocks and two backward glider waves. Ten of these were used to make the first breeder.
: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. It remains by far the smallest known gun. Gosper has since found other guns, see new gun and the p144 gun shown under factory.
........................O........... ......................O.O........... ............OO......OO............OO ...........O...O....OO............OO OO........O.....O...OO.............. OO........O...O.OO....O.O........... ..........O.....O.......O........... ...........O...O.................... ............OO......................
:gourmet (p32) Found by Dave Buckingham 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.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. ....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. This name 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. For examples see double-barrelled, edge shooter, factory, gliderless, Gosper glider gun and new gun.
: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 very fast Life algorithm by Bill Gosper that is designed to take advantage of the considerable amount of repetitive behaviour in many large patterns of interest. This algorithm is described by Gosper in his paper listed in the bibliography at the end of this lexicon. Roughly speaking, the basic idea is to store subpatterns in a hash table so that the results of their evolution don't have to be recomputed if they arise again somewhen, or somewhere, else. Although HashLife stores individual patterns in an economical manner, the fact that it retains earlier generations means that it can require a lot of memory. There is also the problem that it works asynchronously - at any given moment it will usually have evolved different parts of the pattern through different numbers of generations - so it is not suitable for showing a continuous display of the evolution of a pattern.
:hassle See hassler.
:hassler An oscillator that works by hassling (repeatedly moving or changing) some object. For some examples, see Al Jolson, baker's dozen, toad-flipper, toad-sucker and traffic circle.
: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!".)
:heat For an oscillator or spaceship, the average number of cells which change state in each generation. For example, the heat of a glider is 4, because 2 cells are born and 2 die every generation.
For a period n oscillator with an r-cell rotor the heat is at least 2r/n and no more than r(1-(n mod 2)/n). These bounds are equal for n=2 and n=3.
: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 Stephen Silver). 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. See also Herschel loop.
Fifteen simple stable Herschel conduits are currently known, having been discovered from 1995 onwards by Dave Buckingham (DJB) and Paul Callahan (PBC). These are shown in the following table. In this table "steps" is the number of steps, "m" tells how the Herschel is moved (R = turned right, L = turned left, B = turned back, F = unturned, f = flipped), and "dx" and "dy" give the displacement of the centre cell of the Herschel (assumed to start in the orientation shown above).
steps m dx dy discovery ------------------------------------ 64 R -11 9 DJB, Sep 1995 77 Ff -25 -8 DJB, Aug 1996 112 L -12 -33 DJB, Jul 1996 116 F -32 1 PBC, Feb 1997 117 F -40 -6 DJB, Jul 1996 119 Ff -20 14 DJB, Sep 1996 153 Ff -48 -4 PBC, Feb 1997 156 L -17 -41 DJB, Aug 1996 158 Ff -27 -5 DJB, Jul 1996 166 F -49 3 PBC, May 1997 176 Ff -45 0 PBC, Oct 1997 190 R -24 16 DJB, Jul 1996 200 Lf -17 -40 PBC, Jun 1997 202 Rf -7 32 DJB, May 1997 222 Bf 6 -16 PBC, Oct 1998
:Herschel loop A cyclic Herschel track. Although no loop of length less than 256 generations has been constructed it is possible to make oscillators of smaller periods by putting more than one Herschel in the track. In this way oscillators, and in most cases guns, of all periods from 54 onwards can now be constructed (although the p55 case is a bit strange, shooting itself with gliders in order to stabilize itself). See also emu and omniperiodic.
: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. After one generation this is the same as the I-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.
:hook with tail (p1) For a long time this was the smallest still life without a well-established name. It is now a vital component of the smallest known HWSS gun, where it acts as a rock.
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 in 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. After one generation this is the same as the H-heptomino.
OO.. .O.. .OO. ..OO
:IMG = intermitting glider gun
:Immigration A form of colorized Life in which there are two types of ON cell, a newly-born cell taking the type of the majority of its three parent cells and surviving cells remaining of the same type as in the previous generation.
: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. The classic 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 5×5 pattern with infinite growth. This too emits a block-laying switch engine.
OOO.O O.... ...OO .OO.O O.O.O
Following a conjecture of Nick Gotts, Stephen Silver produced, in May 1998, a pattern of width 1 which exhibits infinite growth. This pattern was very large (12470×1 in the first version, reduced to 5447×1 the following day). In October 1998 Paul Callahan did an exhaustive search, finding the smallest example, the 39×1 pattern shown below. This produces two block-laying switch engines.
OOOOOOOO.OOOOO...OOO......OOOOOOO.OOOOO
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).
:initials = monogram
: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..
:intermitting glider gun Despite the name, an intermitting glider gun (IMG) is more often an oscillator than a gun. There are two basic types. A type 1 IMG consists of two guns firing at one another in such a way that each gun is temporarily disabled on being hit by a glider from the other gun. A type 2 IMG consists of a single gun firing at a 180-degree glider reflector in such a way that returning gliders temporarily disable the gun.
Both types of IMG can be used to make glider guns of periods that are multiples of the base period. This is done by firing another gun across the two-way intermittent glider stream of the IMG in such a way that gliders only occasionally escape.
:island The unconnected polyplets of which a stable pattern consists are sometimes called islands. So, for example, a boat has only one island, while an aircraft carrier has two, a honey farm has four and the standard form of the eater3 has five.
...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. In terms of its 7×7 bounding box it ties with trice tongs as the smallest p3 oscillator.
...OO. ..O..O O..O.O O...O. O..... ...O.. .OO...
:Jaws A breeder constructed by Nick Gotts in February 1997. In the original version Jaws had an initial population of 150, which at the time was the smallest for any known pattern with superlinear growth. In November 1997 Gotts produced a 130-cell Jaws using some switch engine predecessors found by Paul Callahan. Jaws has since been beaten by the even smaller mosquitos.
Jaws consists of eight pairs of switch engines which produce a new 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
....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, 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), but no concrete example is known.
By analogy with the corresponding fairy chess pieces we would presumably have also "camelship", "zebraship" and "giraffeship", with displacements of (3,1), (3,2) and (4,1), respectively. But no examples of these are known either.
:Kok's galaxy (p8) Found by Jan Kok in 1971. See converter for a use of this sparker.
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 2 or 3 of the 8 adjacent cells are also ON, and a cell that is OFF will turn ON if and only if exactly 3 of the 8 adjacent cells are ON. (This is more succinctly stated as: "If 2 of your 8 nearest neighbours are ON, don't change. If 3 are ON, turn ON. Otherwise, turn OFF.")
:Life32 A freeware Life program by Johan Bontes for Microsoft Windows 95/98/NT. At the time of writing this is still in beta.
: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 ribbon = superstring
: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 diagram shows an example of a lightspeed wire, with a small defect that travels along it at the speed of light.
....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.... .......................................................... ..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.. .O......O...............................................O. O.OOOOO....OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.O .O.....O................................................O. ..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO.. .......................................................... ....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....
: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 has been proved.
.OO. O..O .O.O ..O.
:loaf on loaf = bi-loaf
:loaf p3 = jam
:loaf pendel = mold
..OO. .O..O O.O.O .O.O. ..O..
: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 shillelagh (p1)
OO..OO O..O.O .OO...
:long ship (p1)
OO.. O.O. .O.O ..OO
:long sinking ship = long canoe
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 evolution 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 in 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.
:Max A name for the smallest known spacefiller. The name represents the fact that the growth rate is the fastest possible. (This has not quite been proved, however. There remains the possibility, albeit not very likely, that a periodic agar could have an average density greater than 1/2, and a spacesfiller stretching such an agar at the same speed as known spacefillers would have a faster average growth rate.)
:mazing (p4) In terms of its minimum cell count of 12 this ties with mold as the smallest p4 oscillator.
...OO.. .O.O... O.....O .O...OO ....... ...O.O. ....O..
:medium fish = MWSS
:metamorphosis II The following p30 glider-to-LWSS converter. This was found by Paul Callahan in 1994. Robert Wainwright independently found it later the same year and gave it its name.
......................O. .....................O.. .....................OOO ........................ ........................ .........O.O............ .........O..O........... OO..........OO.......... OO........O...OO........ .....OO.....OO.......... ....O....O..O........... .........O.O............ ........................ ........................ ........................ ........................ ................O....... ...............OOO...... ..............OOOOO..... .............O.O.O.O.... .............OO...OO.... ........................ ........................ ................O....... ...............O.O...... ...............O.O...... ................O....... ...............OO....... ...............OO....... ...............OO.......
: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. Compare with jam. In terms of its 6×6 bounding box this is the smallest p4 oscillator, but in terms of its minimum cell count of 12 it merely ties with mazing.
...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....
:mosquito See mosquito1, mosquito2. mosquito3 and mosquito4.
:mosquito1 A breeder constructed by Nick Gotts in September 1998. The original version had an initial population of 103, which was then the smallest for any known pattern with superlinear growth (beating the record previously held by Jaws). This was reduced to 97 by Stephen Silver the following month, but was then almost immediately superceded by mosquito2.
Mosquito1 consists of the classic puffer train plus four LWSS and four MWSS (mostly in predecessor form, to keep the population down). Once it gets going it produces a new block-laying switch engine (plus a lot of junk) every 280 generations. It is therefore an MMS breeder, albeit a messy one.
:mosquito2 A breeder constructed by Nick Gotts in October 1998. Its initial population of 85 was at the time the smallest for any known pattern with superlinear growth, but has since been beaten by mosquito3.
Mosquito2 is very like mosquito1, but uses two fewer MWSS and one more LWSS.
:mosquito3 A breeder constructed by Nick Gotts in October 1998. Its initial population of 75 was at the time the smallest for any known pattern with superlinear growth, but has since been beaten by mosquito4.
Mosquito3 has one less LWSS than mosquito2. It is somewhat different from the earlier mosquitos in that the switch engines it makes are glider-producing rather than block-laying.
:mosquito4 A slightly improved version of mosquito3 which Stephen Silver produced in October 1998 making use of another discovery of Nick Gotts (September 1997): an 8-cell pattern that evolves into a LWSS plus some junk. Mosquito4 is a breeder with an initial population of 73, the smallest for any known pattern with superlinear growth. (In the last release of this lexicon this was mentioned as a variant of mosquito3, but Nick Gotts suggested that it deserves its own number.)
:mould = mold
:MSM breeder See breeder.
:multi-state Life = colorized Life
: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 and filter.
.......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 in 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 every period that is a multiple 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 in 1992.
......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 describes 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. (See Herschel loop and emu.)
: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 - see edge shooter for one of these.
.........................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. This was found by Charles Corderman in 1971. 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...
:octomino Any 8-cell polyomino. There are 369 such objects. The word is particularly applied to the following octomino (or its two-generation successor), which is fairly common but lacks a proper name:
..OO ..OO OOO. .O..
: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. If we insist that the oscillator must contain a cell oscillating at the full period, then 33, 34, 39 and 51 must be added to this list.
:onion rings For each integer n>1 onion rings of order n is a stable agar of density 1/2 obtained by tiling the plane with a certain 4n × 4n pattern. The tile for order 3 onion rings is shown below - the reader should then be able to deduce the form of tiles of other orders.
......OOOOOO .OOOO.O....O .O..O.O.OO.O .O..O.O.OO.O .OOOO.O....O ......OOOOOO OOOOOO...... O....O.OOOO. O.OO.O.O..O. O.OO.O.O..O. O....O.OOOO. OOOOOO......
: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, a traffic light predecessor, although not one of the more common ones.
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 non-stable finite patterns. An oscillator is divided into a rotor and a stator. See also omniperiodic.
In general cellular automaton theory the term "oscillator" usually covers spaceships as well, but this usage is not normal in Life.
:overcrowding = overpopulation
:over-exposure = underpopulation
: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).
:parent cells The three cells that cause a new cell to be born.
: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 in 1970 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 f