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

Introduction | Bibliography

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:c = speed of light

:CA = cellular automaton

:caber tosser Any pattern whose population is asymptotic to c.log(t) for some constant c, and 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.

:Cambridge pulsar CP 48-56-72 = pulsar (The numbers refer to the populations of the three phases. The Life pulsar was indeed discovered at Cambridge, like the first real pulsar a few years earlier.)

:Canada goose (c/4 diagonally, p4) Found by Jason Summers, January 1999. It consists of a glider plus a tagalong.

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

At the time of its discovery the Canada goose was the smallest known diagonal spaceship other than the glider, but this record has since been beaten, first by the second spaceship shown under Orion, and more recently by quarter.

:candelabra (p3) By Charles Trawick. See also the note under cap.

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

:candlefrobra (p3) Found by Robert Wainwright in November 1984.

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

The following diagram shows that a pair of these can act in some ways like killer toads. See also snacker.

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

:canoe (p1)

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

:cap The following induction coil. It can also be easily be stabilized to form a p3 oscillator - see candelabra for a slight variation on this.

    .OO.
    O..O
    OOOO

:carnival shuttle (p12) Found by Robert Wainwright in September 1984 (using MW emulators at the end, instead of the monograms shown here).

    .................................O...O
    OO...OO..........................OOOOO
    .O.O.O...O..O......OO...O..O.......O..
    .OO.OO..OO...OO....OO..OO...OO....O.O.
    .O.O.O...O..O......OO...O..O.......O..
    OO...OO..........................OOOOO
    .................................O...O

:carrier = aircraft carrier

:casing That part of the stator of an oscillator which is not adjacent to the rotor. Compare bushing.

:catacryst A 58-cell quadratic growth pattern found by Nick Gotts in April 2000. This was formerly the smallest known pattern with superlinear growth, but has since been superseded by the related metacatacryst. The catacryst consists of three arks plus a glider-producing switch engine. 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.

:caterer (p3) Found by Dean Hickerson, August 1989. Compare with jam. In terms of its minimum population of 12 this is the smallest p3 oscillator. See also double caterer and triple caterer.

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

More generally, any oscillator which serves up a bit in the same manner may be referred to as a caterer.

:Caterpillar A spaceship that works by laying tracks at its front end. The only example constructed to date is a p270 17c/45 spaceship built by Gabriel Nivasch in December 2004, based on work by himself, Jason Summers and David Bell. This Caterpillar has a population of about 12 million in each generation and was put together by a computer program that Nivasch wrote. It is by far the largest and most complex Life object ever constructed.

The 17c/45 Caterpillar is based on the following reaction between a pi-heptomino and a blinker:

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

In this reaction, the pi moves forward 17 cells in the course of 45 generations, while the blinker moves back 6 cells and is rephased. This reaction has been known for many years, but it was only in September 2002 that David Bell suggested that it could be used to build a 17c/45 spaceship, based on a reaction he had found in which pis crawling along two rows of blinkers interact to emit a glider every 45 generations. Similar glider-emitting interactions were later found by Gabriel Nivasch and Jason Summers. The basic idea of the spaceship design is that streams of gliders created in this way can be used to construct fleets of standard spaceships which convey gliders to the front of the blinker tracks, where they can be used to build more blinkers.

A different Caterpillar may be possible based on the following reaction, in which the pattern at top left reappears after 31 generations displaced by (13,1), having produced a new NW-travelling glider. In this case the tracks would be waves of backward-moving gliders.

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

:Catherine wheel = pinwheel

:cauldron (p8) Found in 1971 independently by Don Woods and Robert Wainwright. Compare with Hertz oscillator.

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

:cavity = 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 transition rules, etc.

It is common for the neighbourhood of a cell to be the 3x...x3 (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.

:centinal (p100) Found by Bill Gosper. This combines the mechanisms of the p46 and p54 shuttles (see twin bees shuttle and p54 shuttle).

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

:century (stabilizes at time 103) This is a common pattern which evolves into three blocks and a blinker. In June 1996 Dave Buckingham built a neat p246 glider gun using a century as the engine. See also bookend and diuresis.

    ..OO
    OOO.
    .O..

:chemist (p5)

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

:C-heptomino Name given by Conway to the following heptomino, a less common variant of the B-heptomino.

    .OOO
    OOO.
    .O..

:Cheshire cat A block predecessor by C. R. Tompkins that unaccountably appeared both in Scientific American and in Winning Ways. See also grin.

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

:chicken wire A type of stable agar of density 1/2. The simplest version is formed from the tile:

    OO..
    ..OO

But the "wires" can have length greater than two and need not all be the same. For example:

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

:cigar = mango

:cis-beacon on anvil (p2)

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

:cis-beacon on table (p2)

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

:cis-boat with tail (p1)

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

:cis fuse with two tails (p1) See also pulsar quadrant.

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

:cis-mirrored R-bee (p1)

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

:cis snake = canoe

:clean Opposite of dirty. A reaction which produces a small number of different products which 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.

    ..O.
    O.O.
    .O.O
    .O..

:clock II (p4) Compare with pinwheel.

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

:cloud of smoke = smoke

:cloverleaf This name was given by Robert Wainwright to his p2 oscillator washing machine. But Achim Flammenkamp also gave this name to Achim's p4.

:cluster Any pattern in which each live cell is connected to every other live cell by a path that 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 ship (c/2 orthogonally, p16) A puffer engine discovered by Tim Coe in October 1995.

    ....OOOOOO
    ..OO.....O
    OO.O.....O
    ....O...O.
    ......O...
    ......OO..
    .....OOOO.
    .....OO.OO
    .......OO.

:Coe's p8 (p8) Found by Tim Coe in August 1997.

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

:colorized Life A cellular automaton which is the same as Life except for the use of a number 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:

    OOO
    ..O
    .O.

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.

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

:confused eaters (p4) Found by Dave Buckingham before 1973.

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

:converter A conduit in which the input object is not of the same type as the output object. This term tends to be preferred when either the input object or the output object is a spaceship.

The following diagram shows a p8 pi-heptomino-to-HWSS converter. This was originally found by Dave Buckingham in a larger form (using a figure-8 instead of the boat). The improvement shown here is by Bill Gosper (August 1996). Dieter Leithner has since found (much larger) oscillators of periods 44, 46 and 60 to replace the Kok's galaxy.

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

:convoy A collection of spaceships all moving in the same direction at the same speed.

:Corder- Prefix used for things involving switch engines, after Charles Corderman.

:Corder engine = switch engine

:Cordergun A gun firing Corderships. The first was built by Jason Summers in July 1999, using a glider synthesis by Stephen Silver.

: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 the slowest spaceships so far 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 6. In January 2004, Paul Tooke found the 3-engine Cordership shown below.

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

:cousins (p3) This contains two copies of the stillater rotor.

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

:cover The following induction coil. See scrubber for an example of its use.

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

:covered table = cap

:cow (c p8 fuse)

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

:CP pulsar = pulsar

:crane (c/4 diagonally, p4) The following spaceship found by Nicolay Beluchenko in September 2005, a minor modification of a tubeater found earlier by Hartmut Holzwart. The wing is of the same form as in the swan and Canada goose.

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

:cross (p3) Found by Robert Wainwright in October 1989.

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

In February 1993, Hartmut Holzwart noticed that this is merely the smallest of an infinite family of p3 oscillators. The next smallest member is shown below.

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

:crowd (p3) Found by Dave Buckingham in January 1973.

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

:crown The p12 part of the following p12 oscillator, where it is hassled by caterer, a jam and a HW emulator. This oscillator was found by Noam Elkies in January 1995.

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

:crucible = cauldron

:crystal A regular growth that is sometimes formed when a stream of gliders, or other spaceships, is fired into some junk.

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.

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

:cuphook (p3) Found by Rich Schroeppel, October 1970. This is one of only three essentially different p3 oscillators with only three cells in the rotor. The others are 1-2-3 and stillater.

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

The above is the original form, but it can be made more compact:

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

:curl = loop

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