This list of Game of Life terms is compiled by Stephen A. Silver, for which I am thankful. See the original credit page for all credits. The original Life Lexicon is available at Silver's website. This list is changed by Edwin Martin to work with the Game of Life program. His e-mail address is firstname.lastname@example.org.
This lexicon is prepared for the Game of Life program.
:101 (p5) Found by Achim Flammenkamp in August 1994. The name was suggested by Bill Gosper, noting that the phase shown below displays the period in binary.
:14-ner = fourteener
:17c/45 spaceship A spaceship travelling at 17c/45. No such spaceship has actually been built, but Jason Summers has written up a plan for making one (see http://entropymine.com/jason/life/17c45/). The resulting spaceship would be so huge that building it without the aid of specialized software would be practically impossible.standard spaceships which are used to carry gliders to the front of the blinker trails, where they can be used to build more blinkers.
:2 eaters = two eaters
:4-8-12 diamond The following pure glider generator.
:4 boats (p2)
:4F = Fast Forward Force Field
:Achim's p144 (p144) This was found (minus the blocks shown below) on a cylinder of width 22 by Achim Flammenkamp in July 1994. Dean Hickerson reduced it to a finite form using figure-8s the same day. The neater finite form shown here - replacing the figure-8s with blocks - was found by David Bell in August 1994. See factory for a use of this oscillator.
:Achim's p16 (p16) Found by Achim Flammenkamp, July 1994.
:Achim's p4 (p4) Dave Buckingham found this in a less compact form (using two halves of sombreros) in 1976. The form shown here was found by Achim Flammenkamp in 1988. The rotor is two copies of the rotor of 1-2-3-4, so the oscillator is sometimes called the "dual 1-2-3-4".
:Achim's p5 = pseudo-barberpole
:Achim's p8 (p8) Found by Achim Flammenkamp, July 1994.
:A for all (p6) Found by Dean Hickerson in March 1993.
: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, houndstooth agar, onion rings, squaredance 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.
: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.)
:Al Jolson = Jolson
:almosymmetric (p2) Found in 1971.
:antlers = moose antlers
:ants (p5 wick) The standard form is shown below. It is also possible for any ant to be displaced by one or two cells relative to either or both of its neighbouring ants. Dean Hickerson found fenceposts for both ends of this wick in October 1992 and February 1993. See electric fence, and also wickstretcher.
:anvil The following induction coil.
A lot of known spaceships 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, 1973. The average number of live rotor cells is five (V), which is also the period.
:B = B-heptomino
:B-52 bomber The following p104 double-barrelled glider gun. It uses a B-heptomino and emits one glider every 52 generations. It was found by Noam Elkies in March 1996, except that Elkies used blockers instead of molds, the improvement being found by David Bell later the same month.
: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, the great on-off, the light bulb and the spark coil. The following less trivial example (by Dean Hickerson, August 1997) is the only one known with more than four cells in its rotor. It is p4 and has a 6-cell rotor.
:bakery (p1) A common formation of two bi-loaves.
:barberpole Any p2 oscillator in the infinite sequence bipole, tripole, quadpole, pentapole, hexapole, heptapole ... (It wasn't my idea to suddenly change from Latin to Greek.) This sequence of oscillators was found by the MIT group in 1970. The term is also used (usually in the form "barber pole") to describe other extensible sections of oscillators or spaceships, especially those (usually of period 2) in which all generations look alike except for a translation and/or rotation/reflection.
:barberpole intersection = quad
:barber's pole = barberpole
:basic shuttle = queen bee shuttle
:beacon maker (c p8 fuse)
:beehive and dock (p1)
:beehive on big table = beehive and dock
:beehive pusher = hivenudger
:beehive with tail (p1)
: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 acquired particular importance in 1996 due to Dave Buckingham's work on B tracks - see in particular My Experience with B-heptominos in Oscillators.
:B-heptomino shuttle = twin bees shuttle
:bi-boat = boat-tie
:biclock The following pure glider generator.
:big beacon = figure-8
:big fish = HWSS
:big S (p1)
:big table = dock
:billiard table configuration Any oscillator in which the rotor is enclosed within the stator. Examples include airforce, cauldron, clock II, Hertz oscillator, negentropy, pinwheel, pressure cooker and scrubber.still life: pure glider generator:
:bi-ship = ship-tie
:biting off more than they can chew (p3) Found by Peter Raynham, July 1972.
:Black&White = Immigration
:blasting cap The pi-heptomino (after the shape at generation 1). A term used at MIT and still occasionally encountered.
:blinker puffer Any puffer whose output is blinkers. However, the term is particularly used for p8 c/2 puffers. The first such blinker puffer was found by Robert Wainwright in 1984, and was unexpectedly simple:x66: phase change in the puffer. This fact allows p8 blinker puffers to be used to construct rakes of all periods which are large multiples of four.
:blinkers bit pole (p2) Found by Robert Wainwright, June 1977.
:blinker ship A growing spaceship in which the wick consists of a line of blinkers. An example by Paul Schick based on his Schick engine is shown below. Here the front part is p12 and moves at c/2, 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.
:block and dock (p1)
:block and glider (stabilizes at time 106)
:block on big table = block and dock
:block on table (p1)
The following pattern, in which three gliders push a block one cell diagonally, is an example of how a block puhser works.
: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 then 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 an eater1, converted into a glider which travels back along exactly the same path that is used by the gliders that toggle the boat-bit.)
:boat maker (c p4 fuse)
: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 June 1993. The following example is by Noam Elkies (February 1996) and uses Tim Coe's swan. Note that in any boatstretcher the point of the boat can be removed to get a tubstretcher.
:boat-tie (p1) The name is a pun on "bow tie".
:boss (p4) Found by Dave Buckingham, 1972.
:bounding box The smallest rectangular array of cells that contains the whole of a given pattern. For oscillators and guns this usually is meant to include all phases of the pattern, but excludes, in the case of guns, the outgoing stream(s).
:bow tie = boat-tie
:brain (c/3 orthogonally, p3) Found by David Bell, May 1992.
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=stationary). Typically an MMM breeder is a rake puffer, an MMS breeder is a puffer producing puffers which produce stationary objects (still lifes and/or oscillators), an MSM 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 the metacatacryst.
: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
: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 in the 1970s. The name is due to Bill Gosper.
:bullet heptomino Generation 1 of the T-tetromino.
:burloaf = loaf
:by flops (p2) Found by Robert Wainwright.
:c = speed of light
:CA = cellular automaton
:caber tosser Any pattern whose population is asymptotic to c.log(t) for some constant c, and which contains a glider (or other spaceship) bouncing between a slower receding spaceship and a fixed reflector which emits a spaceship (in addition to the reflected one) whenever the bouncing spaceship hits it.
As the receding spaceship gets further away the bouncing spaceship takes longer to complete each cycle, and so the extra spaceships emitted by the reflector are produced at increasingly large intervals. More precisely, if v is the speed of the bouncing spaceship and u the speed of the receding spaceship, then each interval is (v+u)/(v-u) times as long as the previous one. The population at time t is therefore n.log(t)/log((v+u)/(v-u)) + O(1), where n is the population of one of the extra spaceships (assumed constant).
The first caber tosser was built by Dean Hickerson in May 1991.spaceship other than the glider, but this record has since been beaten, first by the second spaceship shown under Orion, and more recently by the following 25-cell spaceship (Jason Summers, September 2000):
:candlefrobra (p3) Found by Robert Wainwright in November 1984.killer toads. See also snacker.
:carrier = aircraft carrier
:catacryst A 58-cell quadratic growth pattern found by Nick Gotts in April 2000. This was formerly the smallest known pattern with superlinear growth, but has since been superceded by the related metacatacryst. The catacryst consists of three arks plus a glider-producing switch engine. It produces a block-laying switch engine every 47616 generations. Each block-laying switch engine has only a finite life, but the length of this life increases linearly with each new switch engine, so that the pattern overall grows quadratically, as an unusual type of MMS breeder.
:catalyst An object that participates in a reaction but emerges from it unharmed. The term is 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.bit in the same manner may be referred to as a ceterer.
:Catherine wheel = pinwheel
:cavity = eater plug
:cell The fundamental unit of space in the Life universe. The term is often used to mean a live cell - the sense is usually clear from the context.
:cellular automaton A certain class of mathematical objects of which Life is an example. A 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 proper subset of this cube.) This is known as the Moore neighbourhood.
: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 and diuresis.
:cigar = mango
:cis-beacon on anvil (p2)
:cis-beacon on table (p2)
:cis-boat with tail (p1)
:cis-mirrored R-bee (p1)
:cis snake = canoe
:clean Opposite of dirty. A reaction which produces a small number of different products which are desired or which are easily deleted is said to be clean. For example, a puffer which produces just one object per period is clean. Clean reactions are useful because they can be used as building blocks in larger constructions.
When a fuse is said to be clean, or to burn cleanly, this usually means that no debris at all is left behind.
:clock (p2) Found by Simon Norton, May 1970. This is the fifth or sixth most common oscillator, being about as frequent as the pentadecathlon, but much less frequent than the blinker, toad, beacon or pulsar. But it's surprisingly rare considering its small size.
:cloud of smoke = smoke
: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.
:CNWH Conweh, creator of the Life universe.
:Coe's p8 (p8) Found by Tim Coe in August 1997.
: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.
:colour of a glider The colour of a glider is a property of the glider which remains constant while the glider is moving along a straight path, but which can be changed when the glider bounces off a reflector. It is an important consideration when building something using reflectors.
The colour of a glider can be defined as follows. First choose some cell to be the origin. This cell is then considered to be white, and all other cells to be black or white in a checkerboard pattern. (So the cell with coordinates (m,n) is white if m+n is even, and black otherwise.) Then the colour of a glider is the colour of its leading cell when it is in a phase which can be rotated to look like this:
A reflector which does not change the colour of gliders obviously cannot be used to move a glider onto a path of different colour than it started on. But a 90-degree reflector which does change the colour of gliders is similarly limited, as the colour of the resulting glider will depend only on the direction of the glider, no matter how many reflectors are used. For maximum flexibility, therefore, both types of reflector are required.
:complementary blinker = fore and back
: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.
:confused eaters (p4) Found by Dave Buckingham before 1973.
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 periods 44, 46 and 60 to replace the Kok's galaxy.
:Corder- Prefix used for things involving switch engines, after Charles Corderman.
: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). 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.
:covered table = cap
:cow (c p8 fuse)
:CP pulsar = pulsar
:cross (p3) Found by Robert Wainwright in October 1989.
:crowd (p3) Found by Dave Buckingham in January 1973.
:crucible = cauldron
The most common example is initiated by the following collision of a glider with a block. With a glider stream of even period at least 82, this gives a crystal which forms a pair beehives for every 11 gliders which hit it.
:curl = loop
:dart (c/3 ortogonally, p3) Found by David Bell, May 1992.
:de Bruijn diagram = de Bruijn graph
:de Bruijn graph As applied to Life, a de Bruijn graph is a graph showing which pieces can be linked to which other pieces to form form a valid part of a Life pattern of a particular kind.
For example, if we are interested in still lifes, then we could consider 2×3 rectangular pieces and the de Bruijn graph would show which pairs of these can be overlapped to form 3×3 squares in which the centre cell remains unchanged in the next generation.
David Eppstein's search program gfind is based on de Bruijn graphs.
: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.) There are other definitions of density, but this one will do here.
In 1994 Noam Elkies proved that the maximum density of a stable pattern is 1/2, which had been the conjectured value. See the paper listed in the bibliography. Marcus Moore provided a simpler proof in 1995, and in fact proves that a still life with an m × n bounding box has at most (mn+m+n)/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 (Hartmut Holzwart, September 1992).
:D-heptomino = Herschel
:diamond = tub
:diamond ring (p3) Found by Dave Buckingham in 1972.
:diehard Any pattern that vanishes, but only after a long time. The following example 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.
:dinner table (p12) Found by Robert Wainwright in 1972.
:dirty Opposite of clean. A reaction which produces a large amount of complicated junk which is difficult to control or use is said to be dirty. Many basic puffer engines are dirty and need to be tamed by accompanying spaceships in order to produce clean output.
:diuresis (p90) Found by David Eppstein in October 1998. His original stabilization used pentadecathlons. The stabilization with complicated still lifes shown here (in two slightly different forms) was found by Dean Hickerson the following day. The name is due to Bill Gosper (see kidney).
:do-see-do The following reaction, found by David Bell in 1996, in which two gliders appear to circle around each other as they are reflected 90 degrees by a twin bees shuttle. Four copies of the reaction can be used to create a p92 glider loop which repeats the do-see-do reaction forever.
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. (The LWSS version was known at least as early 1994, when Paul Callahan saw it form spontaneously as a result of firing a LWSS stream at some random junk.)
:double ewe (p3) Found by Robert Wainwright before September 1971.
:double wing = moose antlers
:dove The following induction coil.
:down boat with tail = cis-boat with tail
:drain trap = paperclip
:drifter A perturbation moving within a stable pattern. Dean Hickerson has written a program to search for drifters, with the hope of finding one which could be moved around a track. Because drifters can be very small, they could be packed more tightly than Herschels, and so allow the creation of oscillators of periods not yet attained, and possibly prove that Life is omniperiodic. Hickerson has found a number of components towards this end, but it has proved difficult to change the direction of movement of a drifter, and so far no complete track has been found. However, Hickerson has had success using the same search program to find eaters with novel properties, such as that used in diuresis.
:dual 1-2-3-4 = Achim's p4
:early universe Conway's somewhat confusing term for sparse Life.
: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 eater1 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. (In fact the block was the first known eater, being found capable of eating beehives from a queen bee.) Another useful eater is shown below, feasting on a glider.
:eater2 (p1) This eater was found by Dave Buckingham in the 1970s. Mostly it works like the ordinary eater (see eater1) 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.
:eater3 (p1) This large symmetric eater, found by Dave Buckingham, has a very different eating action from the eater1 and eater2. The loaf can take bites out things, being flipped over in the process. The rest of the object merely flips it back again.
: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.
:eater/block frob (p4) Found by Dave Buckingham in 1976 or earlier.
:eater-bound pond = biting off more than they can chew
:eater-bound Z-hexomino = pentoad
:eater eating eater = two eaters
:eater plug (p2) Found by Robert Wainwright, February 1973.
:eaters + = French kiss
:eaters plus = French kiss
:edge-repair spaceship A spaceship which has an edge that possesses no spark and yet is able to perturb things because of its ability to repair certain types of damage to itself. The most useful examples are the following two small p3 c/3 spaceships:Herschel) demonstrates the self-repairing action. T-tetromino component of a c/4 spaceship can also be self-repairing. Stephen Silver noticed that it could be used to delete beehives and, in November 2000, found the smallest known c/4 spaceship with this edge-repair component - in fact, two copies of the component:
: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 June 1994.
:egg = non-spark
:E-heptomino Name given by Conway to the following heptomino.
:elbow ladder Scot Ellison's name for the type of pattern he created in which one or more gliders shuttle back and forth (using the kickback reaction) deleting the output gliders from a pair of slide guns.
:Elkies' p5 (p5) Found by Noam Elkies in 1997.
: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.
:engine The active portion of an object (usually a puffer or gun) which is considered to actually produce its output, and which generally permits no variation in how it works. The other parts of the object are just there to support the engine. For examples, see puffer train, Schick engine, blinker puffer, frothing puffer and line puffer.
:en retard (p3) Found by Dave Buckingham, August 1972.
:Enterprise (c/4 diagonally, p4) Found by Dean Hickerson, March 1993.
: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.
:exposure = underpopulation
:extra extra long = long^4
:extra long = long^3
:extremely impressive (p6) Found by Dave Buckingham, August 1976.
: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 is David Bell's improvement of the one Bill Gosper found in July 1994. The p72 oscillator is by Robert Wainwright, 1990, and the block factory is Achim's p144 minus one of its stabilizing blocks.)
: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).
:Fast Forward Force Field The following reaction found by Dieter Leithner in May 1994. In the absence of the incoming LWSS the gliders would simply annihilate one another, but as shown they allow the LWSS to advance 11 spaces in the course of the next 6 generations. A neat illusion. See also star gate. (Leithner named the Fast Forward Force Field in honour of his favourite science fiction writer, the physicist Robert L. Forward.)
:father = parent
:featherweight spaceship = glider
:Fermat prime calculator A pattern constructed by Jason Summers in January 2000 that exhibits infinite growth if and only if there are no Fermat primes greater than 65537. The question of whether or not it really does exhibit infinite growth is therefore equivalent to a well-known and long-standing unsolved mathematical problem. It will, however, still be growing at generation 102585827975. The pattern is based on Dean Hickerson's primer and caber tosser patterns and a p8 beehive puffer by Hartmut Holzwart.
:F-heptomino Name given by Conway to the following heptomino.
:figure-8 (p8) Found by Simon Norton in 1970.
: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. Another 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.)
:fishhook = eater1
: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.
:flip-flops Another name for the flip-flop shown under phoenix.
: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.
:flying machine = Schick engine
:fox (p2) This is the smallest asymmetric p2 oscillator. Found by Dave Buckingham, July 1977.
:French kiss (p3) Found by Robert Wainwright, July 1971.
:frog II (p3) Found by Dave Buckingham, October 1972.
:frothing puffer A frothing puffer (or a frothing spaceship) is a puffer (or spaceship) whose back end appears to be unstable and breaking apart, but which nonetheless survives. The exhaust festers and clings to the back of the puffer/spaceship before breaking off. The first known frothing puffers were c/2, and most were found by slightly modifying the back ends of p2 spaceships. A number of these have periods which are not a multiple of 4 (as with some line puffers). Paul Tooke has also found c/3 frothing puffers.
The following p78 c/2 frothing puffer was found by Paul Tooke in April 2001.
:frothing spaceship See frothing puffer.
:fumarole (p5) Found by Dean Hickerson in September 1989. In terms of its 7×8 bounding box this is the smallest p5 oscillator.
: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.
:Gabriel's p138 (p138) The following oscillator found by Gabriel Nivasch in October 2002.
:galaxy = Kok's galaxy
:Garden of Eden A configuration of ON and OFF cells that can only occur in generation 0. (This term was first used in connection with cellular automata by John W. Tukey, many years before Life.) It was known from the start that there are Gardens of Eden in Life, because of a theorem by Edward Moore that guarantees their existence in a wide class of cellular automata. Explicit examples have since been constructed, the first by Roger Banks, et al. at MIT in 1971. This example was 9 × 33. In 1974 J. Hardouin-Duparc, et al. produced a 6 × 122 example. The following shows a 14 × 14 example (with 143 ON cells) by Achim Flammenkamp (1991 or 1992).
:generation The fundamental unit of time. The starting pattern is generation 0.
:germ (p3) Found by Dave Buckingham, September 1972.
:gfind A program by David Eppstein which uses de Bruijn graphs to search for new spaceships. It was with gfind that Eppstein found the weekender, and Paul Tooke later used it to find the dragon. It is available at http://www.ics.uci.edu/~eppstein/ca/gfind.c (C source code only).
:GIG A glider injection gate. This is a device for injecting a glider into a glider stream. The injected glider is synthesized from one or more incoming spaceships assisted by the presence of the GIG. (This contrasts with some other glider injection reactions which do not require a GIG.) Gliders already in the glider stream pass through the GIG without interfering with it. A GIG usually consists of a small number of oscillators.
Glider injection gates are useful for building glider guns with pseudo-periods that are of the form nd, where n is a positive integer, and d is a proper divisor of some convenient base gun period (such as 30 or 46), with d > 13.
:glider (c/4 diagonally, p4) The smallest, most common and first discovered spaceship. This was found by Richard Guy in 1970 while Conway's group was attempting to track the evolution of the R-pentomino. The name is due in part to the fact that it is glide symmetric. (It is often stated that Conway discovered the glider, but he himself has said it was Guy. See also the cryptic reference ("some guy") in Winning Ways.)
:glider-block cycle An infinite oscillator based on the following reaction (a variant of the rephaser). The oscillator consists of copies of this reaction displaced 2n spaces from one another (for some n>6) with blocks added between the copies in order to cause the reaction to occur again halfway through the period. The period of the resulting infinite oscillator is 8n-20. (Alternatively, in a cylindrical universe of width 2n the oscillator just consists of two gliders and two blocks.)
:glider construction = glider synthesis
:glider duplicator Any reaction in which one input glider is converted into two output gliders. This can be done either by oscillators or by spaceships. The most useful glider duplicators are those with low periods.
The following period 30 glider duplicator demonstrates a simple glider duplicating mechanism found by Dieter Leithner. The input glider stream comes in from the upper left, and the output glider streams leave at the upper and lower right. One of the output glider streams is inverted, so an inline inverter is required to complete the duplicator.
Spaceship convoys which can duplicate gliders are very useful since they (along with glider turners) provide a means to clean up many dirty puffers by duplicating and turning output gliders so as to impact into the exhaust to clean it up.
Glider duplicators (and turners) are known for backward gliders using p2 c/2 spaceships, and for forward gliders using p3 c/3 spaceships. These are the most general duplicators for these speeds.
:glider injection gate = GIG
:gliderless A gun is said to be gliderless if it does not use gliders. The purist definition would insist that a glider does not appear anywhere, even incidentally. For a long time the only known way to construct LWSS, MWSS and HWSS guns involved gliders, and it was not until April 1996 that Dieter Leithner constructed the first gliderless gun (a p46 LWSS gun). The following diagram shows 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.)
: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.
: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.
:glider synthesis Construction of an object by means of glider collisions. It is generally assumed that the gliders should be arranged so that they could come from infinity - that is, gliders should not have had to pass through one another to achieve the initial arrangement.
Perhaps the most interesting glider syntheses are those of spaceships, because these can be used to create corresponding guns and rakes. Many of the c/2 spaceships that are based on standard spaceships have been synthesized, mostly by Mark Niemiec. In June 1998 Stephen Silver found syntheses for some of the Corderships (although it was not until July 1999 that Jason Summers used this to build a Cordership gun). In May 2000, Noam Elkies suggested that a 2c/5 spaceship found by Tim Coe in May 1996 might be a candidate for glider synthesis. Initial attempts to construct a synthesis for this spaceship got fairly close, but it was only in March 2003 that Summers and Elkies managed to find a way perform the crucial last step. Summers then used the new synthesis to build a c/2 forward rake for the 2c/5 spaceship; this was the first example in Life of a rake which fires spaceships that travel in the same direction as the rake but more slowly.
A 3-glider synthesis of a pentadecathlon is shown in the diagram below. This was found in April 1997 by Heinrich Koenig and came as a surprise, as it was widely assumed that anything using just three gliders would already be known.
:gnome = fox
: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.
:grandfather = grandparent
:great on-off (p2)
:grey counter = Gray counter (This form is erroneous, as Gray is surname, not a colour.)
: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
: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.
:hammerhead A certain front end for c/2 spaceships. The central part of the hammerhead pattern is supported between two MWSS. The picture below shows a small example of a spaceship with a hammerhead front end (the front 9 columns).
:harbor (p5) Found by Dave Buckingham in September 1978. The name is by Dean Hickerson.
: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.
:hashlife A 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 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. This does, however, mean that complex patterns can require substantial amounts of memory. Hashlife provides a means of evolving repetitive patterns millions (or even billions or trillions) of generations further than normal Life algorithms can manage in a reasonable amount of time. It is not, however, suitable for showing a continuous display of the evolution of a pattern, because it works asynchronously - at any given moment it will usually have evolved different parts of the pattern through different numbers of generations.
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). For n=2 and n=3 these bounds are equal.
:heavyweight emulator = HW emulator
:heavyweight spaceship = HWSS
:hebdarole (p7) Found by Noam Elkies, November 1997. Compare fumarole. The smaller version shown below was found soon after by Alan Hensel using a component found by Dave Buckingham in June 1977. The top tens rows can be stabilized by their mirror image (giving an inductor) and this was the original form found by Elkies.
:hectic (p30) Found by Robert Wainwright in September 1984.
: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. The term is due to Bill Gosper.
The following is an example of the kind of reaction used at the heart of a Heisenburp device. The glider at bottom right alters the reaction of the other two gliders without itself being affected in any way.
:heptaplet Any 7-cell polyplet.
Sixteen simple stable Herschel conduits are currently known, having been discovered from 1995 onwards by Dave Buckingham (DJB) and Paul Callahan (PBC). (Of course, the number depends on what is meant by "simple".) 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 125 Bf 9 -17 PBC, Nov 1998 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 ------------------------------------
See also Herschel transceiver.
: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 receiver A pattern found by Paul Callahan in 1996, as part of the first stable glider reflector. Used as a receiver, it converts two parallel input gliders (with path separations of 2, 5, or 6) to an R-pentomino, which is then converted to a Herschel by one of two known mechanisms (the first of which was found by Dave Buckingham way back in 1972, and the second by Stephen Silver in October 1997). The version using Buckingham's R-to-Herschel converter is shown below.
:Herschel transceiver An adjustable Herschel conduit made up of a Herschel transmitter and a Herschel receiver. The intermediate stage consists of two gliders on parallel tracks, so the transmitter and receiver can be separated by any required distance. The conduit may be stable, or may contain low-period oscillators.
:Herschel transmitter Any Herschel-to-glider converter that produces two gliders on parallel tracks which can be used as input to a Herschel receiver. If the gliders are far enough apart, a suitably oriented mirror image of the receiver will also work: the first glider triggers the receiver and the second glider deletes the extra beehive.
The following diagram shows a stable Herschel transmitter found by Paul Callahan in May 1997:
:hexadecimal = beehive and dock
:hexaplet Any 6-cell polyplet.
:hive = beehive
:hivenudger (c/2 orthogonally, p4) A spaceship found by Hartmut Holzwart in July 1992. (The name is due to Bill Gosper.) 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 hivenudgers.
:honey farm (p1) A common formation of four beehives.
:hustler (p3) Found by Robert Wainwright, June 1971.
:hustler II (p4)
:HWSS emulator = HW emulator
: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 glider hotel A pattern by David Bell, named after Hilbert's "infinite hotel" scenario in which a hotel with an infinite number of rooms has room for more guests even if it is already full, simply by shuffling the old guests around.
In this pattern, two pairs of Corderships moving at c/12 are pulling apart such that there is an ever-lengthening glider track between them. Every 128 generations another glider is injected into the glider track, joining the gliders already circulating there. The number of gliders in the track therefore increases without limit.
The tricky part of this construction is that even though all the previously injected gliders are repeatedly flying through the injection point, that point is guaranteed to be empty when it is time for the next glider to be injected.
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.
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.
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, stability being achieved at generation 1483.
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 and a caber tosser.
See also Fermat prime calculator.
:initials = monogram
:inline inverter The following reaction in which a p30 gun can be used to invert the presence or absence of gliders in a p30 stream, with the output glider stream being in the same direction as the input glider stream.
:integral = integral sign
:integral sign (p1)
:intentionless = elevener
:interchange (p2) A common formation of six blinkers.
: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 individual 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.
:J = Herschel
:jack (p4) Found by Robert Wainwright, April 1984.
:jam (p3) Found by Achim Flammenkamp in 1988, but not widely known about until its independent discovery (and naming) by Dean Hickerson in September 1989. 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.
: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, teeth, catacryst and metacatacryst.
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.
:JC = dead spark coil
:JHC John Horton Conway. Also another name for monogram.
:J-heptomino = Herschel
: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.
:killer toads A pair of toads acting together so that they can eat things. Here, for example, are some killer toads eating a HWSS. Similarly they can eat a MWSS (but not a LWSS). For another example see twirling T-tetsons II. See also candlefrobra.
:Klein bottle As an alternative to a torus, it's possible to make a finite Life universe in the form of a Klein bottle. The simplest way to do this is to use an m × n rectangle with the top edge joined to the bottom edge (as for a torus) and the left edge twisted and joined to the right.
:knightship Any spaceship of type (2m,m)/n. Such spaceships do exist (see universal constructor), but no concrete example is known. A knightship must be asymmetric and its period must be at least 6, which makes searching for them using programs like lifesrc very difficult.
By analogy with the corresponding fairy chess pieces, spaceships of types (3m,m)/n, (3m,2m)/n and (4m,m)/n would presumably be called camelships, zebraships and giraffeships, respectively. But no examples of these are known either, and they are even more difficult to search for.
: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):
:Laputa (p2) Found by Rich Schroeppel, September 1992.
: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/ME/NT/2000/XP.
:LifeLab A shareware Life program by Andrew Trevorrow for the Macintosh (MacOS 8.6 or later).
: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.
Although lifesrc itself is a command-line program, Jason Summers has made a GUI version called WinLifeSearch for Microsoft Windows.
The lifesrc algorithm is only useful for very small periods, as the amount of computing power required rises rapidly with increasing period. For most purposes, period 7 is the practical limit with current hardware.
Lifesrc is available from http://www.canb.auug.org.au/~dbell/ (source code only).
:light bulb (p2) Found in 1971.rotor can be embedded in a slightly smaller stator like this:
: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.
:lightweight emulator = LW emulator
:lightweight spaceship = LWSS
: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 archetypal line puffer was found by Alan Hensel in March 1994, based on a spaceship found earlier that month by Hartmut Holzwart. The following month Holzwart found a way to make extensible c/2 line puffers, and Hensel found a much smaller stabilization the following day. But in October 1995 Tim Coe discovered that for large widths these were often unstable, although typically lasting millions of generations. In May 1996, however, Coe 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.
Line puffers have enabled the construction of various difficult periods for c/2 spaceships and puffers, including occasionally periods which are not multiples of 4 and which would therefore be impossible to attain with the usual type of construction based on standard spaceships. (See frothing puffer for another method of constructing such periods.) In particular, the first c/2 rake with period not divisible by 4 was achieved in January 2000 when David Bell constructed a p42 backrake by means of line puffers.
See also puff suppressor.
:loading dock (p3) Found by Dave Buckingham, September 1972.
:loaf on loaf = bi-loaf
:loaf siamese barge (p1)
:LoM = lumps of muck
:lone dot agar An agar in which every live cell is isolated in every generation.
:lonely bee = worker bee
:long A term applied to an object that is of the same basic form as some standard object, but longer. For examples see long barge, long boat, long bookend, long canoe, long shillelagh, long ship and long snake.
:long barge (p1)
:long boat (p1)
:long canoe (p1)
:long hat = loop
:long hook = long bookend
:long house = dock
:long integral (p1)
:long long barge (p1)
:long long boat (p1)
:long long canoe (p1)
:long long ship (p1)
:long long snake (p1)
:long shillelagh (p1)
:long ship (p1)
:long sinking ship = long canoe
:long snake (p1)
: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.
:LWSS emulator = LW emulator
:LWTDS Life Worker Time Deficiency Syndrome. Term coined by Dieter Leithner to describe the problem of having to divide scarce time between Life and real life.
:LW volcano = toaster
:mathematician (p5) Found by Dave Buckingham, 1972.
: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 the known spacefillers would have a faster average growth rate.)
:mazing (p4) In terms of its minimum population of 12 this ties with mold as the smallest p4 oscillator. Found by Dave Buckingham in December 1973. For some constructions using mazings, see popover and sixty-nine.
:medium fish = MWSS
:metacatacryst A 52-cell pattern exhibiting quadratic growth. Found by Nick Gotts, December 2000. This is currently the smallest known pattern (in terms of initial population) with superlinear growth. See also catacryst.
:metamorphosis An oscillator built by Robert Wainwright that uses the following reaction (found by Bill Gosper) to turn gliders into LWSS, and converts these LWSS back into gliders by colliding them head on. (There are in fact two ways to do the following reaction, because the spark of the twin bees shuttle is symmetric.)
:metamorphosis II An oscillator built by Robert Wainwright in December 1994 based on the following p30 glider-to-LWSS converter. This converter was first found by Paul Rendell, January 1986 or earlier, but wasn't widely known about until Paul Callahan rediscovered it in December 1994.
:Mickey Mouse (p1) A name proposed by Mark Niemiec for the following still life:
:middleweight emulator = MW emulator
:middleweight spaceship = MWSS
: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.
:mod The smallest number of generations it takes for an oscillator or spaceship to reappear in its original form, possibily subject to some rotation or reflection. The mod may be equal to the period, but it may also be a quarter of the period (for oscillators that rotate 90 degrees every quarter period) or half the period (for other oscillators which rotate 180 degrees every half period, and also for flippers).
:mold (p4) Found by Achim Flammenkamp in 1988, but not widely known until Dean Hickerson rediscovered it (and named it) in August 1989. Compare with jam. In terms of its minimum population of 12 it ties with mazing as the smallest p4 oscillator. But in terms of its 6×6 bounding box it wins outright. In fact, of all oscillators that fit in a 6×7 box it is the only one with period greater than 2.
:monogram (p4) Found by Dean Hickerson, August 1989.
:moose antlers (p1)
: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 for a couple of hours the smallest for any known pattern with superlinear growth, but was then beaten by mosquito3.
: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 was beaten a few days later by mosquito4.
: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, at the time the smallest for any known pattern with superlinear growth, but superceded a few days later by mosquito5.
:mosquito5 A slightly improved version of mosquito4 which Nick Gotts produced in October 1998. The improvement is of a similar nature to the improvement of mosquito4 over mosquito3. Mosquito5 is a breeder with an initial population of 71. At the time, this was the smallest population for any known pattern with superlinear growth, but it has since been superceded by teeth, catacryst and metacatacryst.
:mould = mold
:MSM breeder See breeder.
:multi-state Life = colorized Life
: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 bipole, the blinker, the clock, the cuphook, the Gray counter, the quad, the scrubber, the skewed quad and the p2 snake pit. The following diagram shows a p2 example (by Dean Hickerson, May 1993) with a larger rotor. See ring of fire for a very large one.
: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 which Rott had found in November 1993 (but which was not widely known until Paul Callahan rediscovered it in June 1994) 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.
:MW volcano (p5) Found by Dean Hickerson in April 1992.
: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.
: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 five (p3) Found by Dean Hickerson, January 1990.
: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.
: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.
:n-omino Any polyomino with exactly n cells.
:non-monotonic A spaceship is said to be non-monotonic if its leading edge falls back in some generations. The first example (shown below) was found found by Hartmut Holzwart in August 1992. This is p4 and travels at c/4. In April 1994, Holzwart found examples of p3 spaceships with this property, and this is clearly the smallest possible period. Another non-monotonic spaceship is the weekender.
:octagon II (p5) The first known p5 oscillator, discovered in 1971 independently by Sol Goodman and Arthur Taber. The name is due to the latter.
:octagon IV (p4) Found by Robert Wainwright, January 1979.
: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:
:omino = polyomino
: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 in 1996 (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, 31, 37, 38, 41, 43 and 53. If we insist that the oscillator must contain a cell oscillating at the full period, then 34 and 51 should be added to this list. The most recently achieved periods were all found by Noam Elkies: p49 in August 1999 (a glider loop using p7 reflectors built from his new p7 pipsquirter), p39 (previously only possible without a p39 cell) in July 2000, and p27 in November 2002.
: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.
:Orion (c/4 diagonally, p4) Found by Hartmut Holzwart, April 1993.
:orphan Conway's preferred term for a Garden of Eden.
:overcrowding = overpopulation
:over-exposure = underpopulation
:overweight spaceship = OWSS
:Ox A 1976 novel by Piers Anthony which involves Life.
:p = period
:p30 shuttle = queen bee shuttle
:p46 shuttle = twin bees shuttle
:pair of bookends = bookends
:pair of tables = table on table
:parent cells The three cells that cause a new cell to be born.
:PD = pentadecathlon
:penny lane (p4) Found by Dave Buckingham, 1972.
: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. In fact it is the fifth or sixth most common oscillator overall, being about as frequent as the clock, but much less frequent than the blinker, toad, beacon or pulsar.polyomino in more than one phase.
:pentant (p5) Found by Dave Buckingham, July 1976.
:pentaplet Any 5-cell polyplet.
:pentomino Any 5-cell polyomino. There are 12 such patterns, and Conway assigned them all letters in the range O to Z, loosely based on their shapes. Only in the case of the R-pentomino has Conway's label remained in common use, but all of them can nonetheless be found in this lexicon.
:period The smallest number of generations it takes for an oscillator or spaceship to reappear in its original form. The term can also be used for a puffer, wick, fuse, superstring, stream of spaceships, factory or gun. In the last case there is a distinction between true period and pseudo period. There is also a somewhat different concept of period for wicktrailers.
:perturb To change the fate of an object by reacting it with other objects. Typically, the other objects are sparks from spaceships or oscillators, or are eaters or impacting spaceships. Perturbations are typically done to turn a dirty reaction into a clean one, or to change the products of a reaction. In many desirable cases the perturbing objects are not destroyed by the reaction, or else are easily replenished.
:phase A representative generation of a periodic object such as an oscillator or spaceship. The number of phases is equal to the period of the object. The phases of an object usually repeat in the same cyclic sequence forever, although some perturbations can cause a phase change.
:phase change A perturbation of a periodic object which causes the object to skip ahead by one or more phases. If the perturbation is repeated indefinitely, this can effectively change the period of the object. An example of this, found by Dean Hickerson in November 1998, is shown below. In this example, the period of the oscillator would be 7 if the mold were removed, but the period is increased to 8 because of the repeated phase changes caused by the mold's spark.spaceship found by Jason Summers, in which the phase is changed as it deletes a forward glider. This phase change allows the spaceship to be used to delete a glider wave produced by a rake whose period is 2 (mod 4).
Phase changing reactions have enabled the construction of spaceships having periods that were otherwise unknown, and also allow the construction of period-doubling and period-tripling convoys to easily produce very high period rakes.
See also blinker puffer.
:phi The following common spark. The name comes from the shape in the generation after the one shown here.
:phoenix Any pattern all of whose cells die in every generation, but which never dies as a whole. A spaceship cannot be a phoenix, and in fact every finite phoenix eventually evolves into an oscillator. The following 12-cell oscillator (found by the MIT group in December 1971) is the smallest known phoenix, and is sometimes called simply "the phoenix".
:pi = pi-heptomino
:pincers = great on-off
:pipsquirt = pipsquirter
:pipsquirter An oscillator that produces a domino spark that is orientated parallel to the direction from which it is produced (in contrast to domino sparkers like the pentadecathlon and HWSS, which produce domino sparks perpendicular to the direction of production). The following is a small p6 example found by Noam Elkies in November 1997.
:pi ship A growing spaceship in which the back part consists of a pi-heptomino travelling at a speed of 3c/10. The first example was constructed by David Bell. All known pi ships are too large to show here, but the following diagram shows how the pi fuse works.
:piston (p2) Found in 1971.
:pixel = cell
:plet = polyplet
:polyomino A finite collection of orthogonally connected cells. The mathematical study of polyominoes was initiated by Solomon Golomb in 1953. Conway's early investigations of Life and other cellular automata involved tracking the histories of small polyominoes, this being a reasonable way to ascertain the typical behaviour of different cellular automata when the patterns had to be evolved by hand rather than by computer. Polyominoes have no special significance in Life, but their extensive study during the early years lead to a number of important discoveries and has influenced the terminology of Life. (Note on spelling: As with "dominoes" the plural may also be spelt without an e. In this lexicon I have followed Golomb in using the longer form.)
It is possible for a polyomino to be an oscillator. In fact there are infinitely many examples of such polyominoes, namely the cross and its larger analogues. The only other known examples are the block, the blinker, the toad, the star and (in two different phases) the pentadecathlon.
:population The number of ON cells.
:PPS (c/5 orthogonally, p30) A pre-pulsar spaceship. Any of three different p30 c/5 orthogonal spaceships in which a pre-pulsar is pushed by a pair of spiders. The back sparks of the spaceship can be used to perturb gliders in many different ways, allowing the easy construction of c/5 puffers. The first PPS was found by David Bell in May 1998 based on a p15 pre-pulsar spaceship found by Noam Elkies in December 1997. See also SPPS and APPS.
:precursor = predecessor
:predecessor Any pattern that evolves into a given pattern after one or more generations.
:pre-pulsar A common predecessor of the pulsar, such as that shown below. This duplicates itself in 15 generations. (It fails, however, to be a true replicator because of the way the two copies then interact.)
A pair of tubs can be placed to eat half the pre-pulsar as it replicates; this gives the p30 oscillator Eureka where the pre-pulsar's replication becomes a movement back and forth. (See twirling T-tetsons II for a variation on this idea.) By other means the replication of the pre-pulsar can be made to occur in just 14 generations as half of it is eaten; this allows the construction of p28 and p29 oscillators, and is in fact the only known method for creating a p29 oscillator. The pre-pulsar is also a vital component of the only known p47 oscillator.
See also PPS.
:pre-pulsar spaceship See PPS.
:protein (p3) Found by Dave Buckingham, November 1972.
:pseudo Opposite of true. A gun emitting a period n stream of spaceships (or rakes) is said to be a pseudo period n gun if its mechanism oscillates with a period different from n. This period will necessarily be a multiple of n. Pseudo period n glider guns are known to exist for all periods greater than or equal to 14, with smaller periods being impossible. The first pseudo p14 gun was built by Dieter Leithner in 1995.
Exactly the same distinction between true and pseudo also exists for puffers.
:pseudo-random glider generator An object which emits a random-looking stream of gliders, like the sequence of bits from a pseudo-random number generator. Pseudo-random glider generators contain gliders or other spaceships in a loop with a feedback mechanism which causes later spaceships to interfere with the generation of earlier spaceships. The period can be very high, since a loop of n spaceships has 2n possible states.
The first pseudo-random glider generator was built by Bill Gosper. David Bell built the first moving one in 1997, using c/3 rakes.
:pseudo still life The strict definition of still life rules out such stable patterns as the bi-block. In such patterns there are dead cells which have more than 3 neighbours in total, but fewer than 3 in any component still life. These patterns are called pseudo still lifes. Mark Niemiec has enumerated the pseudo still lifes up to 24 bits, and his figures are shown below.
------------- Bits Number ------------- 8 1 9 1 10 7 11 16 12 55 13 110 14 279 15 620 16 1645 17 4067 18 10843 19 27250 20 70637 21 179011 22 462086 23 1184882 24 3068984 -------------
:puffer An object that moves like a spaceship, except that it leaves debris behind. The first known puffers were found by Bill Gosper and travelled at c/2 orthogonally (see diagram below for the very first one, found in 1971). Not long afterwards c/12 diagonal puffers were found (see switch engine). Discounting wickstretchers (which are not puffers in the conventional sense), no new velocity was obtained after this until David Bell found the first c/3 orthogonal puffer in April 1996. Since then c/5 orthogonal puffers have also been found, the first by Tim Coe in May 1997. Jason Summers built the first c/4 orthogonal puffer in January 1999, and the first 2c/5 orthogonal puffer in February 1999.
:puffer engine A pattern which can be used as the main component of a puffer. The pattern may itself be a puffer (e.g. the classic puffer train), it may be a spaceship (e.g. the Schick engine), or it may even be unstable (e.g. the switch engine).
:puffer train The full name for a puffer, coined by Conway before any examples were known. The term was also applied specifically to the classic puffer train found by Bill Gosper and shown below. This is very dirty, and the tail does not stabilize until generation 5533. It consists of a B-heptomino (shown here one generation before the standard form) escorted by two LWSS. (This was the second known puffer. The first is shown under puffer.)
:puff suppressor An attachment at the back of a line puffer that suppresses all or some of its puffing action. The example below (by Hartmut Holzwart) has a 3-cell puff suppressor at the back which suppresses the entire puff, making a p2 spaceship. If you delete this puff suppressor then you get a p60 double beehive puffer. Puff suppressors were first recognised by Alan Hensel in April 1994.
:pulsar (p3) Despite its size, this is the fourth most common oscillator (and by far the most common of period greater than 2) and was found very early on by Conway. See also pre-pulsar and pulsar quadrant.
:pulsar 18-22-20 = two pulsar quadrants
:pulsar quadrant (p3) This consists of a quarter of the outer part of a pulsar stabilized by a cis fuse with two tails. This is reminiscent of mold and jam. Found by Dave Buckingham in July 1973. See also two pulsar quadrants.
Also another name for a pulsar quadrant.
The following diagram shows a p5 glider pulse divider by Dieter Leithner (February 1998). The first glider moves the centre block and is reflected at 90 degrees. The next glider to come along will not be reflected, but will move the block back to its original position. The small size and low period of this example make it useful for constructing glider guns of certain periods. p7, p22, p36 and p46 versions of this pulse divider are also known.
:pulshuttle V (p30) Found by Robert Wainwright, May 1985. Compare Eureka.
:pure glider generator A pattern that evolves into one or more gliders, and nothing else. There was some interest in these early on, but they are no longer considered important. Here's a neat example:
:pyrotechnecium (p8) Found by Dave Buckingham in 1972.
:pyrotechneczum A common mistaken spelling of pyrotechnecium, caused by a copying error in the early 1990s.
:python = long snake
:Q = Quetzal
:QuadLife A form of colorized Life in which there are four types of ON cell. A newly-born cell takes the type of the majority of its three parent cells, or the remaining type if its parent cells are all of different types. In areas where there are only two types of ON cell QuadLife reduces to Immigration.
:quapole = quadpole
:quasar (p3) Found by Robert Wainwright, August 1971. See pulsar.
:queen bee shuttle (p30) Found by Bill Gosper in 1970. There are a number of ways to stabilize the ends. Gosper originally stabilized shuttles against one another in a square of eight shuttles. Two simpler methods are shown here; for a third see buckaroo. The queen bee shuttle is the basis of all known true p30 guns (see Gosper glider gun).
:Quetzal Dieter Leithner's name for the true p54 glider gun he built in January 1998. (This is short for Quetzalcoatlus and expresses the fact that the gun was a very large Herschel loop that was not an emu.) Shortly afterwards Leithner also built a p56 Quetzal using a mechanism found by Noam Elkies for this purpose. In October 1998 Stephen Silver constructed a p55 Quetzal using Elkies' p5 reflector of the previous month.
Some of the more recent Quetzals are not Herschel loops, but are instead short Herschel tracks firing several glider streams all but one of which is reflected back to the beginning of the track to create a new Herschel. Noam Elkies first had the idea of doing this for the p55 case, and Stephen Silver constructed the resulting gun shortly after building the original (much larger) p55 Quetzal. Jason Summers later built a p54 version, which is more complicated because the evenness of the period makes the timing problems considerably more difficult.
:quilt = squaredance
:R = R-pentomino
:R2D2 (p8) This was found, in the form shown below, by Peter Raynham in the early 1970s. The name derives from a form with a larger and less symmetric stator discovered by Noam Elkies in August 1994. Compare with Gray counter.
:r5 = R-pentomino
:rake Any puffer whose debris consists of spaceships. A rake is said to be forwards, backwards or sideways according to the direction of the spaceships relative to the direction of the rake. Originally the term "rake" was applied only to forwards c/2 glider puffers (see space rake). Many people prefer not to use the term in the case where the puffed spaceships travel parallel or anti-parallel to the puffer, as in this case they do not rake out any significant region of the Life plane (and, in contrast to true rakes, these puffers cannot travel in a stream, and so could never be produced by a gun).
Although the first rakes (circa 1971) were c/2, rakes of other velocities have since been built. Dean Hickerson's construction of Corderships in 1991 made it easy for c/12 diagonal rakes to be built, although no one actually did this until 1998, by which time David Bell had constructed c/3 and c/5 rakes (May 1996 and September 1997, respectively). Jason Summers constructed a 2c/5 rake in June 2000 (building on work by Paul Tooke and David Bell) and a c/4 orthogonal rake in October 2000 (based largely on reactions found by David Bell).
The smallest possible period for a rake is probably 7, as this could be achieved by a 3c/7 orthogonal backwards glider puffer. The smallest period attained to date is 8 (Jason Summers, March 2001) - see backrake.
:$rats (p6) Found by Dave Buckingham, 1972.
:R-bee = bun
:receiver See Herschel receiver.
:reflector Any stable or oscillating pattern that can reflect some type of spaceship (usually a glider) without suffering permanent damage. The first known reflector was the pentadecathlon, which functions as a 180-degree glider reflector (see relay). Other examples include the buckaroo, the twin bees shuttle and some oscillators based on the traffic jam reaction. Glider guns can also be made into reflectors, although these are mostly rather large.
In September 1998 Noam Elkies found some fast small-period glider reflectors. The p8 version is shown below. Replacing the figure-8 by the p6 pipsquirter gives a p6 version. A more complicated construction allows a p5 version (which, as had been anticipated, soon led to a true p55 gun - see Quetzal). And in August 1999 Elkies found a suitable p7 sparker, allowing the first p49 oscillator to be constructed.
Stable reflectors are special in that if they satisfy certain conditions they can be used to construct oscillators of all sufficiently large periods. It was known for some time that stable reflectors were possible (see universal constructor), but no one was able to construct an explicit example until Paul Callahan did so in October 1996.
All known stable reflectors are very slow. Callahan's original reflector has a repeat time of 4840, soon improved to 1686 and then 894 and then 850. In November 1996 Dean Hickerson found a variant in which this is reduced to 747. Dave Buckingham reduced it to 672 in May 1997 using a somewhat different method, and in October 1997 Stephen Silver reduced it to 623 by a method closer to the original. In November 1998 Callahan reduced this to 575 with a new initial reaction. A small modification by Silver a few days later brought this down to 497.
But in April 2001 Dave Greene found a 180-degree stable reflector with a repeat time of only 202 (see boojum reflector). This reflector also won the $100 prize that Dieter Leithner had offered in April 1997 for the first stable reflector to fit in a 50×50 box, and the additional $100 that Alan Hensel had offered in January 1999 for the same feat. Dave Greene has subsequently offered $50 for the first 90-degree stable glider reflector that fits in a 50×50 box, and a further $50 for the first in a 35×35 box.
See also glider turner.
:relay Any oscillator in which spaceships (typically gliders) travel in a loop. The simplest example is the p60 one shown below using two pentadecathlons. Pulling the pentadecathlons further apart allows any period of the form 60+120n to be achieved - this is the simplest proof of the existence of oscillators of arbitrarily large period.
:repeat time The minimum number of generations that is possible between the arrival of one object and the arrival of the next. This term is used for things such as reflectors or conduits and the objects (gliders or Herschels, for example) will interact fatally with each other (or one will interact fatally with a disturbance caused by the other) if they are too close together. For example, the repeat time of Dave Buckingham's 59-step B-heptomino to Herschel conduit (shown under conduit) is 58.
:rle Run-length encoded. Run-length encoding is a simple (but not very efficient) method of file compression. In Life the term refers to a specific ASCII encoding used for Life patterns (and patterns for other similar cellular automata). This encoding was introduced by Dave Buckingham and is now the usual means of exchanging Life patterns (especially large ones) by e-mail.
:rock Dean Hickerson's term for an eater which remains intact throughout the eating process. The snake in Dave Buckingham's 59-step B-to-Herschel conduit (shown under conduit) is an example. Other still lifes that sometimes act as rocks include the tub, the hook with tail, the eater1 (eating with its tail) and the hat (in Heinrich Koenig's stabilization of the twin bees shuttle).
:roteightor (p8) Found by Robert Wainwright in 1972.
:R-pentomino This is by far the most active polyomino with less than six cells: all the others stabilize in at most 10 generations, but the R-pentomino does not do so until generation 1103, by which time it has a population of 116.
:rule 22 Wolfram's rule 22 is the 2-state 1-D cellular automaton in which a cell is ON in the next generation if and only if exactly one of its three neighbours is ON in the current generation (a cell being counted as a neighbour of itself). This is the behaviour of Life on a cylinder of width 1.
:sawtooth Any finite pattern whose population grows without bound but does not tend to infinity. (In other words, the population reaches new heights infinitely often, but also infinitely often drops below some fixed value.) The first such pattern was constructed by Dean Hickerson in April 1991. Conway's preferred plural is "sawteeth".
:SBM = sliding block memory
:Schick engine (c/2 orthogonally, p12) This spaceship, found by Paul Schick in 1972, produces a large spark (the 15 live cells at the rear in the phase shown below) which can be perturbed by other c/2 spaceships to form a variety of puffers. The diagram below shows the smallest form of the Schick engine, using two LWSS. It is also possible to use two MWSS or two HWSS, or even a LWSS and a HWSS.
:Schick ship = Schick engine
:scrubber (p2) Found in 1971.
:SE = switch engine
:second glider domain The second glider domain of an edge shooter is the set of displacements (in space and time, relative to the glider stream emitted by the edge shooter) that a glider stream may have without interfering with the edge shooter. This is useful to know, because edge shooters are often used to generate glider streams very close to other glider streams.
:ship (p1) The term is also used as a synonym of spaceship.
:ship on boat = ship tie boat
:ship on ship = ship-tie
:ship tie boat (p1)
:shuttle Any oscillator which consists of an active region moving back and forth between stabilizing objects. The most well-known examples are the queen bee shuttle (which has often been called simply "the shuttle") and the twin bees shuttle. See also p54 shuttle and Eureka. Another example is the p72 R-pentomino shuttle that forms part of the pattern given under factory.
:siamese 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 sharing two or more cells. See snake siamese snake and loaf siamese barge for examples.
:sidecar A small tagalong for a HWSS that was found by Hartmut Holzwart in 1992. The resulting spaceship (shown below) has a phase with only 24 cells, making it in this respect the smallest known spaceship other than the standard spaceships and some trivial two-spaceship flotillas derived from them. Note also that a HWSS can support two sidecars at once.
:side-shooting gun = slide gun
:side-tracking See universal constructor.
:signal Movement of information through the Life universe. Signals can be carried by spaceships, fuses, drifters, or conduits. Spaceships can only transfer a signal at the speed of the spaceship, while fuses can transfer a signal at speeds up to the speed of light.
In practice, many signals are encoded as the presence or absence of a glider (or other spaceship) at a particular point at a particular time. Such signals can be combined by the collision of gliders to form logic operations such as AND, OR, and NOT gates. Signals can be duplicated using glider duplicators or other fanout devices, and can be used up by causing perturbations on other parts of the Life object.
:Silver's p5 (p5) The following oscillator found by Stephen Silver in February 2000:
:singular flip flop (p2) Found by Robert Wainwright, July 1972.
:sinking ship = canoe
:six Ls (p3) This is a compact form of loading dock.
:sixty-nine (p4) Found by Robert Wainwright, October 1978.
:skewed quad (p2)
:skewed traffic light (p3) Found by Robert Wainwright, August 1989.
:slide gun A gun which fires sideways from an extending arm. The arm consists of streams of spaceships which are pushing a pattern away from the body of the gun and releasing an output spaceship every time they do so. Each output spaceship therefore travels along a different path.
Dieter Leithner constructed the first slide gun in July 1994 (although he used the term "side shooting gun"). The following pattern shows the key reaction of this slide gun. The three gliders shown will push the block one cell diagonally, thereby extending the length of the arm by one cell, and at the same time they release an output glider sideways. (In 1999, Jason Summers constructed slide guns using other reactions.)
In Conway's original formulation (as part of his proof of the existence of a universal computer in Life) 2 gliders were used to pull the block inwards by three diagonal spaces, and 30 gliders were used to push it out by the same amount. Dean Hickerson later greatly improved on this, finding a way to pull a block inwards by one diagonal space using 2 gliders, and push it out using 3 gliders. In order for the memory to be of any use there also has to be a way to read the value held. It suffices to be able to check whether the value is zero (as Conway did), or to be able to detect the transition from one to zero (as Hickerson did).
Dean Hickerson's sliding block memory is used in Paul Chapman's URM.
:small fish = LWSS
:small lake (p1) See also lake.
:smiley (p8) Found by Achim Flammenkamp in July 1994 and named by Alan Hensel.
:SMM breeder See breeder.
:smoking ship A spaceship which produces smoke. If the smoke extends past the edge of the rest of the spaceship, then it can be used to perturb other objects as the spaceship passes by. Running gliders into the smoke is often a good way to turn or duplicate the them, or convert them into other objects. Sometimes the smoke from a smoking ship may itself be perturbed by accompanying spaceships in order to form a puffer. A simple example of a smoking ship is the Schick engine.domino spark largely inaccessible, but the snacker is extensible, as shown in the next diagram, and so a more accessible p9 domino spark can be obtained. In April 1998 Dean Hickerson found an alternative stabilizer that is less obtrusive than the original one, and this is also shown in this diagram. candlefrobras, although this isn't efficient.
:snake bit An alternative name for a boat-bit. Not a very sensible name, because various other things can be used instead of a snake.
:snake bridge snake (p1)
:snake dance (p3) Found by Robert Wainwright, May 1972.
:snake siamese snake (p1)
:sombreros (p6) Found by Dave Buckingham in 1972. If the two halves are moved three spaces closer to one another then the period drops to 4, and the result is just a less compact form of Achim's p4. Compare also siesta.
:soup A random initial pattern, often assumed to cover the whole Life universe.
:space dust A part of a spaceship or oscillator which looks like a random mix of ON and OFF cells. It is usually very difficult to find a glider synthesis for an object that consists wholly or partly of space dust.
:spacefiller Any pattern that grows at a quadratic rate by filling space with an agar. The first example was found in September 1993 by Hartmut Holzwart, following a suggestion by Alan Hensel. The diagram below shows a smaller spacefiller found by Tim Coe. See also Max. Spacefillers can be considered as breeders (more precisely, MMS breeders), but they are very different from ordinary breeders. The word "spacefiller" was suggested by Harold McIntosh and soon became the accepted term.
:spaceship Any finite pattern that reappears (without additions or losses) after a number of generations and displaced by a non-zero amount. By far the most natural spaceships are the glider, LWSS, MWSS and HWSS. For further examples see big glider, brain, Canada goose, Coe ship, Cordership, dart, dragon, ecologist, edge-repair spaceship, Enterprise, flotilla, fly, hammerhead, hivenudger, non-monotonic, Orion, puff suppressor, pushalong, Schick engine, sidecar, snail, still life tagalong, sparky, swan, turtle, wasp, weekender and x66.
It is known that there exist spaceships travelling in all rational directions and at arbitrarily slow speeds (see universal constructor). Before 1989, however, the only known examples travelled at c/4 diagonally (gliders) or c/2 orthogonally (everything else). In 1989 Dean Hickerson started to use automated searches to look for new spaceships, and had considerable success. Other people have continued these searches using tools such as lifesrc and gfind, and as a result we now have a great variety of spaceships travelling at ten different velocities. The following table details the discovery of spaceships with new velocities.
--------------------------------------------- Speed Direction Discoverer Date --------------------------------------------- c/4 diagonal Richard Guy 1970 c/2 orthogonal John Conway 1970 c/3 orthogonal Dean Hickerson Aug 1989 c/4 orthogonal Dean Hickerson Dec 1989 c/12 diagonal Dean Hickerson Apr 1991 2c/5 orthogonal Dean Hickerson Jul 1991 c/5 orthogonal Tim Coe Jan 1996 2c/7 orthogonal David Eppstein Jan 2000 c/6 orthogonal Paul Tooke Apr 2000 c/5 diagonal Jason Summers Nov 2000 ---------------------------------------------
In addition, Jason Summers has put together a fairly detailed description of how to build a 17c/45 spaceship, although the construction has not yet been carried out. See 17c/45 spaceship for more details.
A period p spaceship which displaces itself (m,n) during its period, where m>=n, is said to be of type (m,n)/p. It was proved by Conway in 1970 that p>=2m+2n. (This follows immediately from the easily-proved fact that a pattern cannot advance diagonally at a rate greater than one half diagonal step every other generation.)
The following diagram shows the only known c/5 diagonal spaceship (Jason Summers, November 2000).
:Spaceships in Conway's Life A series of articles posted by David Bell to the newsgroup comp.theory.cell-automata during the period August-October 1992 that described many of the new spaceships found by himself, Dean Hickerson and Hartmut Holzwart. Bell produced an addendum covering more recent developments in 1996.
:spark A pattern that dies. The term is typically used to describe a collection of cells periodically thrown off by an oscillator or spaceship, but other dying patterns, particulary those consisting or only one or two cells (such as produced by certain glider collisions, for example), are also described as sparks. For examples of small sparks see unix and HWSS. For an example of a much larger spark see Schick engine.
:spark coil (p2) Found in 1971.
:sparse Life This refers to the study of the evolution of a Life universe which starts off as a random soup of extremely low density. Such a universe is dominated at an early stage by blocks and blinkers (often referred to collectively as blonks) in a ratio of about 2:1. Much later it will be dominated by simple infinite growth patterns (presumably mostly switch engines). The long-term fate of a sparse Life universe is less certain. It may possibly become dominated by self-reproducing patterns (see universal constructor), but it is not at all clear that there is any mechanism for these to deal with the all junk produced by switch engines.
:speed of light A speed of one cell per generation, the greatest speed at which any effect can propagate.
:S-pentomino Conway's name for the following pentomino, which rapidly dies.
:spider (c/5 orthogonally, p5) This is the smallest known c/5 spaceship, and was found by David Bell in April 1997. Its side sparks have proved very useful in constructing c/5 puffers, including rakes. See also pre-pulsar.
:spiral (p1) Found by Robert Wainwright in 1971.
:squirter = pipsquirter
:S-spiral = big S
:stamp collection A collection of oscillators (or perhaps other Life objects) in a single diagram, displaying the exhibits much like stamps in a stamp album. The classic examples are by Dean Hickerson (see http://www.math.ucdavis.edu/~dean/RLE/stamps.html).
:star (p3) Found by Hartmut Holzwart, February 1993.
:stator The cells of an oscillator that are always on. Compare rotor. (The stator is sometimes taken to include also some of those cells which are always off.) The stator is divided into the bushing and the casing.
By analogy, the cells of an eater that remain on even when the eater is eating are considered to constitute the stator of the eater. This is not necessarily well-defined, because the eater may have more than one eating action.
:still life Any stable pattern, usually assumed to be finite and nonempty. For the purposes of enumerating still lifes this definition is, however, unsatisfactory because, for example, any pair of blocks would count as a still life, and there would therefore be an infinite number of 8-bit still lifes. For this reason a stricter definition is often used, counting a stable pattern as a single still life only if its islands cannot be divided into two nonempty sets both of which are stable in their own right. Compare pseudo still life.
The requirement that a still life not be decomposable into two separate stable patterns may seem a bit arbitrary, as it does not rule out the possibility that it might be decomposable into more than two. This is shown by the patterns in the following diagram, both found by Gabriel Nivasch in July 2001. On the left is a 32-cell pattern that can be broken down into three stable pieces but not into two. On the right is a 34-cell pattern that can be broken down into four stable pieces but not into two or three. (Note that, as a consequence of the Four-Colour Theorem, four is as high as you need ever go.) It is arguable that patterns like these ought not to be considered as single still lifes.
Still lifes have been enumerated by Conway (4-7 bits), Robert Wainwright (8-10 bits), Dave Buckingham (11-13 bits), Peter Raynham (14 bits) and Mark Niemiec (15-24 bits). The resulting figures are shown below. (These figures shouldn't be affected by the above discussion of the strict definition of "still life", because it is unlikely that there are any doubtful cases with much less than 32 cells.)
------------- Bits Number ------------- 4 2 5 1 6 5 7 4 8 9 9 10 10 25 11 46 12 121 13 240 14 619 15 1353 16 3286 17 7773 18 19044 19 45759 20 112243 21 273188 22 672172 23 1646147 24 4051711 -------------
:strict volatility A term suggested by Noam Elkies in August 1998 for the proportion of cells involved in a period n oscillator which themselves oscillate with period n. For prime n this is the same as the ordinary volatility.
:super beehive = honeycomb
:superstring An infinite orthogonal row of cells stabilized on one side so that it moves at the speed of light, often leaving debris behind. The first examples were found in 1971 by Edward Fitzgerald and Robert Wainwright. Superstrings were studied extensively by Peter Rott during 1992-1994, and he found examples with many different periods. (But no odd periods. In August 1998 Stephen Silver proved that odd-period superstrings are impossible.)
Sometimes a finite section of a superstring can be made to run between two tracks ("waveguides"). This gives a fuse which can be made as wide as desired. The first example was found by Tony Smithurst and uses tubs. (This is shown below. The superstring itself is p4 with a repeating section of width 9 producing one blinker per period and was one of those discovered in 1971. With the track in place, however, the period is 8. This track can also be used with a number of other superstrings.) Shortly after seeing this example, in March 1997 Peter Rott found another superstring track consisting of boats. At present these are the only two waveguides known. Both are destroyed by the superstring as it moves along - it would be interesting to find one that remains intact.
See titanic toroidal traveler for another example of a superstring.
:support Those parts of an object which are only present in order to keep the rest of the object (such an engine or an edge spark) working correctly. These can be components of the object, or else accompanying objects used to perturb the object. In many cases there is a wide variation of support possible for an engine. The arms in many puffers are an example of support.
:surprise (p3) Found by Dave Buckingham, November 1972.
The switch engine was discovered by Charles Corderman in 1971. He also found the two basic types of stabilized switch engine: a p288 block-laying type (the more common of the two) and p384 glider-producing type. These two puffers are the most natural infinite growth patterns in Life, being the only ones ever seen to occur from random starting patterns.
:synthesis = glider synthesis
:T = T-tetromino
:table on table (p1)
:tag = tagalong
:tagalong An object which is not a spaceship in its own right, but which can be attached to one or more spaceships to form a larger spaceship. For examples see Canada goose, fly, pushalong, sidecar and sparky. See also Schick engine, which consists of a tagalong attached to two LWSS (or similar).
:tame To perturb a dirty reaction using other patterns so as to make it clean and hopefully useful. Or to make a reaction work which would otherwise fail due to unwanted products which interfere with the reaction.
:taming See tame.
:technician (p5) Found by Dave Buckingham, January 1973.
:technician finished product = technician
:teeth A 65-cell quadratic growth pattern found by Nick Gotts in March 2000. This (and a related 65-cell pattern which Gotts found at about the same time) beat the record previously held by mosquito5 for smallest population known to have superlinear growth. Now superceded by catacryst and metacatacryst.
:ternary reaction Any reaction between three objects. In particular, a reaction in which two gliders from one stream and one glider from a crossing stream of the same period annihilate each other. This can be used to combine two glider guns of the same period to produce a new glider gun with double the period.
:test tube baby (p2)
:tetraplet Any 4-cell polyplet.
:The Recursive Universe A popular science book by William Poundstone (1985) dealing with the nature of the universe, illuminated by parallels with the game of Life. This book brought to a wider audience many of the results that first appeared in LifeLine. It also outlines the proof of the existence of a universal constructor in Life first given in Winning Ways.
:thumb A spark-like protrusion which flicks out in a manner resembling a thumb being flicked.
Here are two examples. On the left is a p9 thumb sparker found by Dean Hickerson in October 1998. On the right is a p4 one found by David Eppstein in June 2000.
:thunderbird (stabilizes at time 243)
:tick = generation
:TL = traffic light
:T-nosed p6 (p6) Found by Achim Flammenkamp in September 1994. There is also a much larger and fully symmetric version found by Flammenkamp in August 1994.
:toad-flipper A toad hassler that works in the manner of the following example. Two domino sparkers, here pentadecathlons, apply their sparks to the toad in order to flip it over. When the sparks are applied again it is flipped back. Either or both domino sparkers can be moved down two spaces from the position shown and the toad-flipper will still work, but because of symmetry there are really only two different types. Compare toad-sucker.
:toad-sucker A toad hassler that works in the manner of the following example. Two domino sparkers, here pentadecathlons, apply their sparks to the toad in order to shift it. When the sparks are applied again it is shifted back. Either or both domino sparkers can be moved down two spaces from the position shown and the toad-sucker will still work, but because of symmetry there are really only three different types. Compare toad-flipper.
:toaster (p5) Found by Dean Hickerson, April 1992.
:torus As applies to Life, usually means a finite Life universe which takes the form of an m × n rectangle with the bottom edge considered to be joined to the top edge and the left edge joined to the right edge, so that the universe is topologically a torus. There are also other less obvious ways of obtaining an toroidal universe.
See also Klein bottle.
:total aperiodic Any finite pattern which evolves in such a way that no cell in the Life plane is eventually periodic. The first example was found by Bill Gosper in November 1997. A few days later he found the following much smaller example consisting of three copies of a p12 backrake by Dave Buckingham.
:traffic circle (p100)
:traffic jam Any traffic light hassler, such as traffic circle. The term is also applied to the following reaction, used in most traffic light hasslers, in which two traffic lights interact in such a way as to reappear after 25 generations with an extra 6 spaces between them.
:traffic light (p2) A common formation of four blinkers.
:trans-beacon on table (p2)
:trans-boat with tail (p1)
:transceiver See Herschel transceiver.
:trans-loaf with tail (p1)
:transmitter See Herschel transmitter.
:transparent block reaction A certain reaction between a block and a Herschel predecessor in which the block reappears in its original place some time later, the reaction having effectively passed through it. This reaction was found by Dave Buckingham in 1988. It has been used in some Herschel conduits, and in the gunstars. Because the reaction involves a Herschel predecessor rather than an actual Herschel, the following diagram shows instead a B-heptomino (which by itself would evolve into a block and a Herschel).
:transparent debris effect A reaction in which a Herschel or other active region destroys a still life, then later, having passed through the place where the still life was, recreates the still life in its original position. For an example, see transparent block reaction.
:tritoad (p3) Found by Dave Buckingham, October 1977.
:true Opposite of pseudo. A gun emitting a period n stream of spaceships (or rakes) is said to be a true period n gun if its mechanism oscillates with period n. (The same distinction between true and pseudo also exists for puffers.) True period n guns are known to exist for all periods greater than 61 (see My Experience with B-heptominos in Oscillators), but only a few smaller periods have been achieved, namely 22, 24, 30, 44, 46, 48, 50, 54, 55, 56 and 60. (Credits for these small period guns are: p30, p46 and p60 by Bill Gosper in 1970-1971, p44 by Dave Buckingham in 1992, p50 by Dean Hickerson in 1996, p24 and p48 by Noam Elkies in 1997, p54 and p56 by Dieter Leithner in early 1998, p55 by Stephen Silver in late 1998 and p22 by David Eppstein in 2000.)
The following diagram shows the p22 gun (David Eppstein, August 2000, using two copies of a p22 oscillator found earlier the same day by Jason Summers).
:tubber (p3) Found by Robert Wainwright before June 1972..
:tubstretcher See boatstretcher.
:tub with tail (p1)
:tugalong = tagalong
:Turing machine See universal computer.
:turning toads (p4 wick) Found by Dean Hickerson, October 1989.
:turtle (c/3 orthogonally, p3) Found by Dean Hickerson.
:twin bees shuttle (p46) Found by Bill Gosper in 1971, this is the basis of all known p46 oscillators, and so of all known true p46 guns (see new gun for an example). There are numerous ways to stabilize the ends, two of which are shown in the diagram. On the left is David Bell's double block reaction (which results in a shorter, but wider, shuttle than usual), and on the right is the stabilization by a single block. This latter method produces a very large spark which is useful in a number of ways (see, for example, metamorphosis). Adding a symmetrically placed block below this one suppresses the spark. See also p54 shuttle.
:twin peaks = twinhat
:two eaters (p3) Found by Bill Gosper, September 1971.
:unit Life cell A rectangular pattern, of size greater than 1×1, that can simulate Life in the following sense. The pattern by itself represents a dead Life cell, and some other pattern represents a live Life cell. When the plane is tiled by these two patterns (which then represent the state of a whole Life universe) they evolve, after a fixed amount of time, into another tiling of the plane by the same two patterns which correctly represents the Life generation following the one they initially represented. It is usual to use capital letters for the simulated things, so, for example, for the first known unit Life cell (constructed by David Bell in January 1996), one Generation is 5760 generations, and one Cell is 500×500 cells.
:universal computer A computer that can compute anything that is computable. (The concept of computability can be defined in terms of Turing machines, or by Church's lambda calculus, or by a number of other methods, all of which can be shown to lead to equivalent definitions.) The relevance of this to Life is that both Bill Gosper and John Conway proved early on that it is possible to construct a universal computer in the Life universe. (To prove the universality of a cellular automaton with simple rules was in fact Conway's aim in Life right from the start.) Conway's proof is outlined in Winning Ways, and also in The Recursive Universe.
Until recently, no universal Life computer had ever been built in practice, because it would be enormous, even with the improvements that have been devised since those early proofs. In April 2000, Paul Rendell completed a Turing machine construction which can be seen at http://rendell.server.org.uk/gol/tm.htm. This, however, has a finite tape, as opposed to the infinite tape of a true Turing machine, and is therefore not a universal computer. But in November 2002, Paul Chapman announced the construction of a universal computer, details of which can be found at http://www.igblan.com/ca/. This is a universal register machine based around Dean Hickerson's sliding block memory.
See also universal constructor.
:universal constructor A pattern that is capable of constructing almost any pattern that has a glider synthesis. This definition is a bit vague. A precise definition seems impossible because it has not been proved that all possible glider fleets are constructible. In any case, a universal constructor ought to be able to construct itself in order to qualify as such. An outline of Conway's proof that such a pattern exists can be found in Winning Ways, and also in The Recursive Universe. The key mechanism for the production of gliders with any given path and timing is known as side-tracking, and is based on the kickback reaction. A universal constructor designed in this way can also function as a universal destructor - it can delete almost any pattern that can be deleted by gliders.
A universal constructor is most useful when attached to a universal computer, which can be programmed to control the constructor to produce the desired pattern of gliders. In what follows I will assume that a universal constructor always includes this computer.
The existence of a universal constructor/destructor has a number of theoretical consequences.
For example, the constructor could be programmed to make copies of itself. This is a replicator.
The constructor could even be programmed to make just one copy of itself translated by a certain amount and then delete itself. This would be a (very large, very high period) spaceship. Any translation is possible (except that it must not be too small), so that the spaceship could travel in any direction. It could also travel slower than any given speed, since we could program it to perform some time-wasting task (such as repeatedly constructing and deleting a block) before copying itself. Of course, we could also choose for it to leave some debris behind, thus making a puffer.
It is also possible to show that the existence of a universal constructor implies the existence of a stable reflector. This proof is not so easy, however, and is no longer of much significance now that explicit examples of such reflectors are known.
:universal destructor See universal constructor.
:universal register machine = URM
:universal regulator A regulator in which the incoming gliders are aligned to period 1, that is, they have arbitrary timing (subject to some minimum time required for the regulator to recover from the previous glider).
Paul Chapman constructed the first universal regulator in March 2003. It is adjustable, so that the output can be aligned to any desired period.
:unix (p6) Two blocks eating a long barge. This is a useful sparker, found by Dave Buckingham in February 1976. The name derives from the fact that it was for some time the mascot of the Unix lab of the mathematics faculty at the University of Waterloo.
:up boat with tail = trans-boat with tail
:U-pentomino Conway's name for the following pentomino, which rapidly dies.
:vacuum Empty space. That is, space containing only dead cells.
:very long = long long
:very long house The following induction coil.
:volatility The volatility of an oscillator is the size (in cells) of its rotor divided by the sum of the sizes of its rotor and its stator. In other words, it is the proportion of cells involved in the oscillator which actually oscillate. For many periods there are known oscillators with volatility 1, see for example Achim's p16, figure-8, Kok's galaxy, mazing, pentadecathlon, phoenix, relay, smiley and tumbler. The smallest period for which the existence of such statorless oscillators is undecided is 3, although Dean Hickerson showed in 1994 that there are p3 oscillators with volatility arbitrarily close to 1 (as is the case for all but finitely many periods, because of the possibility of feeding the gliders from a true period n gun into an eater).
The term "volatility" is due to Robert Wainwright. See also strict volatility.
:washing machine (p2) Found by Robert Wainwright before June 1972.
:wavefront (p4) Found by Dave Buckingham, 1976 or earlier.
:waveguide See superstring.
:weekender (2c/7 orthogonally, p7) Found by David Eppstein in January 2000. In April 2000 Stephen Silver found a tagalong for a pair of weekenders. At present, n weekenders pulling n-1 tagalongs constitute the only known spaceships of this speed or period.
:weld To join two or more still lifes or oscillators together. This is often done in order to fit the objects into a smaller space than would otherwise be possible. The simplest useful example is probably the integral sign, which can be considered as a pair of welded eater1s.
:Wheels, Life, and other Mathematical Amusements One of Martin Gardner's books (1983) that collects together material from his column in Scientific American. The last three chapters of this book contain all the Life stuff.
:why not (p2) Found by Dave Buckingham, July 1977.
:wickstretcher A spaceship-like object which stretches a wick that is fixed at the other end. The wick here is assumed to be in some sense connected, otherwise most puffers would qualify as wickstretchers. The first example of a wickstretcher was found in October 1992 (front end by Hartmut Holzwart and back end by Dean Hickerson) and stretches ants at a speed of c/4. This is shown below with an improved back end found by Hickerson the following month.boatstretcher). In March 1999 Jason Summers constructed a very large c/12 wickstretcher using switch engine based puffers found earlier by Dean Hickerson. The wick in this last case is the simplest possible one: a single line of diagonal cells. In July 2000 Summers also constructed a c/2 wickstretcher, stretching a p50 traffic jam wick. This was based on an earlier (October 1994) pattern by Hickerson.
:wicktrailer Any extensible tagalong, that is, one which can be attached to the back of itself, as well as to the back of a spaceship. The number of generations which it takes for the tagalong to occur again in the same place is often called the period of the wicktrailer - this has little relation to the period of the tagalong units themselves.
:windmill (p4) Found by Dean Hickerson, November 1989.
:Winning Ways A two-volume book (1982) by Elwyn Berlekamp, John Conway and Richard Guy on mathematical games. The last chapter of the second volume concerns Life, and outlines a proof of the existence of a universal constructor.
:WLS = WinLifeSearch
:worker bee (p9) Found by Dave Buckingham in 1972. Unlike the similar snacker this produces no sparks, and so is not very important. Like the snacker, the worker bee is extensible - it is, in fact, a finite version of the infinite oscillator which consists of six ON cells and two OFF cells alternating along a line. Note that Dean Hickerson's new snacker ends also work here.
:x66 (c/2 orthogonally, p4) Found by Hartmut Holzwart, July 1992. Half of this can be escorted by a HWSS. The name refers to the fact that every cell (live or dead) has at most 6 live neighbours (in contrast to spaceships based on LWSS, MWSS or HWSS). In fact this spaceship was found by a search with this restriction.
:Xlife A popular freeware Life program that runs under the X Window System. The main Life code was written by Jon Bennett, and the X code by Chuck Silvers.
:Y-pentomino Conway's name for the following pentomino, which rapidly dies.
:Z-pentomino Conway's name for the following pentomino, which rapidly dies.
David I. Bell, Spaceships in Conway's Life. Series of articles posted on comp.theory.cell-automata, Aug-Oct 1992. Now available from his web-site.
David I. Bell, Speed c/3 Technology in Conway's Life, 17 December 1999. Available from his web-site.
Elwyn R. Berlekamp, John H. Conway and Richard K. Guy, Winning Ways for your Mathematical Plays, II: Games in Particular. Academic Press, 1982.
David J Buckingham, Some Facts of Life. BYTE, December 1978.
Dave Buckingham, My Experience with B-heptominos in Oscillators. 12 October 1996. Available from Paul Callahan's web-site.
David J. Buckingham and Paul B. Callahan, Tight Bounds on Periodic Cell Configurations in Life. Experimental Mathematics 7:3 (1998) 221-241. Available at http://www.expmath.org/restricted/7/7.3/callahan.ps.gz.
Noam D. Elkies, The still-Life density problem and its generalizations, pp228-253 of "Voronoi's Impact on Modern Science, Book I", P. Engel, H. Syta (eds), Institute of Mathematics, Kyiv 1998 = Vol.21 of Proc. Inst. Math. Nat. Acad. Sci. Ukraine, math.CO/9905194.
Martin Gardner, Wheels, Life, and other Mathematical Amusements. W. H. Freeman and Company, 1983.
R. Wm. Gosper, Exploiting Regularities in Large Cellular Spaces. Physica 10D (1984) 75-80.
N. M. Gotts and P. B. Callahan, Emergent structures in sparse fields of Conway's 'Game of Life', in Artificial Life VI: Procedings of the Sixth International Conference on Artificial Life, MIT Press, 1998.
Mark D Niemiec, Life Algorithms. BYTE, January 1979.
William Poundstone, The Recursive Universe. William Morrow and Company Inc., 1985.
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