Definitions of Life Terms

Life

Life is a cellular automata invented by professor John Horton Conway in the early 1970's.

The universe is an infinitely large array of square cells. Each cell can be in one of two distinct states: dead or alive, empty or full, 0 or 1, etc. Each cell is adjacent to eight other neighbouring cells:

In every generation, a cell changes state according to its current state and the state of its eight neighbours:

If a cell is dead, and has exactly three living neighbours, it becomes alive (a birth).
If a cell is dead, and has less than three or more than three living neighbours, it remains dead.
If a cell is alive, and has two or three living neighbours, it remains alive.
If a cell is alive, and has less than two or more than three living neighbours, it dies.

All cells change state simultaneously. By successively repeating this operation, patterns evolve.

Most of the other definitions on this page apply not only to Life, but also to other cellular automata with different states, neighbourhoods or transition rules.

Patterns are usually characterized by their behavior:

Type I (still-lifes): these patterns have no births and no deaths, and never change.
Type II (oscillators): these patterns evolve through a fixed sequence of states and eventually return to their original state.
Type III (spaceships): these patterns evolve through a fixed sequence of states and eventually return to their original state, but translated in space, moving at a constant velocity.
Type IV: these patterns constantly increase in population:
- Type IVa (guns): these are oscillators which emit spaceships each cycle.
- Type IVb (puffers): these are spaceships which leave behind still-lifes, oscillators, and/or spaceships each cycle.
- Type IVc (breeders): these patterns increase their population quadratically:
  - MMM (moving/moving/moving) breeders: puffers which emit puffers which emit spaceships
  - MMS (moving/moving/still) breeders: puffers which emit puffers which emit still-lifes and/or oscilllators
  - MSM (moving/still/moving) breeders: puffers which emit guns which emit spaceships
  - SMM (still/moving/moving) breeders: guns which shoot puffers which emit spaceships
- Other gun/puffer combinations which which expand at other rates
Type V (unstable): these patterns evolve through a sequence of states which never return to the original state. Small patterns which last a long time before stabilizing are called metheuselahs.

Object

An object is a pattern consisting of one or more closely-connected living cells. In order to provide an unambiguous method of distinguish objects from non-objects, the definition of 'close' is defined precisely:

Any living cell forms an object.
If two objects contains any cells which are neighbours of each other, they are a single connected object. In Life, this includes any living cells adjacent to each other either orthogonally or diagonally.
If two un-connected objects interact with each other so that they cause births which would otherwise not occur, or suppress births which would otherwise occur, they form a single spatially-connected object.

Carrier [4] Block on table (10.25) [4] Up bun on snake (13.221) [7] MWSS on MWSS #1 [7] Glider- blinker collision [3]
If two un-connected objects are adjacent to each other in such a way that they do not affect each other, they do not automatically form an object; these form a pseudo-object.

Block on block [2] Down Snake below snake [8] Block on beacon [4] HWSS on HWSS #3 [7]
If three or more un-connected objects are adjacent to each other in such a way that there exists any way of partitioning these objects into two distinct sets, such that the combined objects in one set do not affect the combined objects in the other set, these objects do not automatically form a single object, even if there is some partition in which they do affect one another. They form a pseudo-object.

Four blocks [4] Two blocks on snake siamese snake [18]

When dealing with periodic objects over their entire lifespan, such as oscillators and spaceships, if any components form an single object together in any generation, they are considered to form a single object in all generations. (This only applies when considering all generations as a whole; when only considering a single generation at a time, this rule is not applicable.)

Pentade- cathlon on pentade- cathlon #7 [8]

HWSS on HWSS #7 [7]

LWSS on OWSS on LWSS #1 [12]

The above also applies, even if the interaction between individual components is completely trivial, either forming attachents between dying cells, or creating additional births which die unobtrusively, or suppressing births which would otherwise die unobtrusively.

Pentade- cathlon on pentade- cathlon #4 [8] Eater eating pentade- cathlon [6] Two blockers [16] Two unices [14] HWSS on HWSS #4 [6]

Pseudo-object

An pseudo-object is a pattern which, although not quite meeting the criteria necessary to be a single object, is nevertheless closely connected.

If two un-connected objects are adjacent to one another in such a way that any empty cells between then do not cause new births, but have a neighbourhood which could form a birth if some if its cells were removed (in Life, this means four or more neighbours), the objects combine to form a pseudo-object.

Still-life

A still-life is an object in which all cells survive, and no new births are formed.

Block [2]

Carrier [6]

Block on table (10.25) [4]

Super beehive (12.121) [6]

Paperclip (14.79) [3]

Moose antlers (15.243) [4]

Small lake (20.88034) [10]

Pseudo-still-life

A pseudo-still-life is a pseudo-object in which all cells survive, and no new births are formed.

Block on block [2]

Down snake below snake [8]

Block on block on block [4]

Block on block on block on block [6]

Two blocks on snake siamese snake [18]

Oscillator

An oscillator is an object which, after several generations, returns to its original state. Objects which return to their original state in 1 generation are still-lifes, and are not considered oscillators.

Terms used to describe motors can also describe parts of oscillators:

The rotor consists of the cells of the oscillator which change from generation to generation.
The stator consists of the cells of the oscillator which never change (which also includes vital dead cells).
The bushing is the part of the stator which borders on the rotor, and affects its function.
The casing is the part of the stator which does not touch the rotor, and which is used to support the bushing.
Sparks are dying cells which are emitted by an oscillator which have no effect on its function, but which are sometimes useful for other purposes, such as modifying other oscillators.
Eggs are thrown off like sparks, but do not die, so they must normally be removed or supporessed by some other means.

Oscillators are often classified by their form or function:

A flip-flop is a period-2 oscillator in which all rotor cells die from underpopulation.
An on-off is a period-2 oscillator in which all rotor cells die from overpopulation. Some period-2 oscillators combine both flip-flop and on-off components.
An phoenix is an oscillator in which every living cell dies in every generation.
A pulsator is a larger-period oscillator with the rotor on the outside.
An inductor is a pulsator with a line of symmetry which is used to suppress births.
A billiard table configuration (BTC) is a larger-period oscillator with the stator on the outside.
A shuttle is a larger-period oscillator with no stator, in which the oscillator moves from place to place during the course of its oscillation, typically being rotated or reflected in the process.
A sparker is an oscillator which throws off sparks which are useful for building other oscillators, etc.
A hassler is an oscillator whose rotor creates projections which can affect other oscillators without being damaged.
An eater-bound oscillator has an object which is attacked by one or more still-life eaters which affect its behavior. Common eaters are the block, tub, and eater.
An sparked oscillator is has an object which is attacked by one or more sparkers which affect its behavior.
An hassled oscillator is an object whose behavior is altered by one or more other objects, including eaters, sparkers, or hasslers.
An babbling brook is an oscillator whose rotor consists of a string of single bits connected end to end. (A muttering moat is similar, with the ends joined together). These oscillators are equivalent to one-dimensional cellular automata.

Blinker [2] (flip- flop, muttering moat)

Beacon [3] (on-off, babbling brook)

Phoenix [10] (flip- flop, phoenix)

Caterer [11] (puls- ator, hassler)

Tumbler [8] (puls- ator, in- ductor)

Hertz oscillator [11] (BTC)

Al Jolson [13] (sparked)

Buckaroo [6] (shuttle, eater- bound, sparker)

Loaf hassled by two blocks and two caterers [52] (eater- bound, hassled)

Pseudo-oscillator

An oscillator is an pseudo-object which, after several generations, returns to its original state. Pseudo-objects which return to their original state in 1 generation are pseudo-still-lifes, and are not considered pseudo-oscillators.

Up toad on toad [6]

Block on beacon [4]

Pentade- cathlon on pentade- cathlon #3 [7]

Spaceship

An spaceship is an object which, after several generations, returns to its original state, but translated in space. Objects which return to their original state without moving are oscillators, and are not considered spaceships.

Glider [2]

Light- weight space- ship (LWSS) [3]

Middle- weight space- ship (MWSS) [3]

Heavy- weight space- ship (HWSS) [3]

LWSS on Coe ship [8]

Sidecar on HWSS [8]

HWSS on (un- named) [x]

Schick ship behind two LWSS [10]

LWSS on OWSS on LWSS #1 [12]

Pseudo-spaceship

An pseudo-spaceship is an pseudo-object which, after several generations, returns to its original state, but translated in space. Pseudo-objects which return to their original state without moving are pseudo-oscillators, and are not considered pseudo-spaceships.

LWSS on LWSS [7]

LWSS on HWSS #8 [7]

HWSS on HWSS #3 [7]

Spaceship flotilla

An spaceship flotilla is a collection of two or more spaceships travelling in tandem. Some of the spaceships may escort mechanisms which are not able to travel by themselves, or they may interact trivially with each other.

LWSS on MWSS #3 [7]

LWSS on Coe ship [8]

Sidecar on HWSS [8]

HWSS on (un- named) [x]

LWSS on OWSS on LWSS #1 [12]

Spaceship Gun

An spaceship gun is an oscillator which emits spaceships. The population of a gun increases linearly with time.
Guns which emit puffer trains are called breeders, and have a population which increases quadratically with time.

Period 30 glider gun	Period 46 glider gun
Period 30 LWSS factory

Puffer Train

An puffer train is a spaceship which emits debris, which may be anything which does not move with the same velocity as the puffer train, such as still-lifes, oscillators, or spaceships. Puffer trains which leave spaceship guns or other puffer trains are breeders, and have a population which increases quadratically with time. Puffer trains which leave no debris are considered spaceships, and are generally not considered with other puffers; however, such clean puffers can often be sparked to produce debris, and are thus often form the basis for larger puffers.

Corderman's block-laying switch engine [5]

Wainwright's P8 puffer [10]

Buckingham's P24 puffer [9]

Gosper's P20 puffer [9]

Breeder

An puffer is a pattern whose population increases forever, and whose population is greater than a linear function of time. Breeders are generally factories which build producers which produce debris, and their population normally increases quadratically with respect to time. The four categories of breeders are categorized by which of the three parts are stationary:

SMM breeder (stationary factory): guns which builds puffer trains which emit spaceships
MSM breeder (stationary producer): puffer trains which build guns which emit spaceships (this is the first type of breeder ever built)
MMS breeder (stationary debris): puffer trains which build puffer trains which emit still-lifes and/or oscillators
MMM breeder (nothing stationary): puffer trains which build puffer trains which emit spaceships

There are also many other hybrid categories possible, including many variations whose population increases at other rates.

Induction coil

An induction coil is an object which, by itself, would produce several unwanted births on its outside. These births can be suppressed by placing another object beside the induction coil. This birth-suppression is referred to as induction.

Table

Side

Bun

Cover

Teardrop

Cuphook

Eater eating long bookend

Very long house

Constellation

A constellation is a collection of several periodic objects or pseudo-objects. Since there are so many possible constellations (for example, there are an infinite number of arrangements of two blocks), most constellations are not interesting. Exceptions include constellations which occur naturally, or which have some functional significance.

Loaf and tub and block and blinker [2]

Fleet [3]

Honey- farm [2]

Bakery [3]

Metheuselah

A metheuselah is a small unstable object which lives for an unusually long time before becoming stable. In Life, this is formally defined as any object of 8 bits or less which survives at least 50 generations before becoming stable. In these pages, this definition is relaxed somewhat to also include some larger long-lived objects or pseudo-objects, or even patterns which are neither, and focuses on the results (which can be obtained from several predecessors), rather than dwelling on specific predecessors.

Gliders by the dozen [3]

Rabbits [5]

Two glider mess [2]

See also: definitions, structure, credits.

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