Class three cellular automata

From LifeWiki
Jump to: navigation, search

Class three cellular automata, according to the classification system of Stephen Wolfram, are those where most patterns tend towards chaotic, seemingly infinite growth. They are thus the polar opposite of class one CA. The term explosive is frequently applied to these rules or patterns in them.

The definition of "most" is not exact. Several class three rules have only been identified as such in retrospect, having been previously considered class four; since most small patterns may in fact stabilize. An early example is 34 Life. Arguably HighLife may be an example as well, as the small natural replicator means that sufficiently large patterns tend towards infinite growth.

A subdivision, not quite exact, could be made between class three rules that produce "active" chaos, and those that produce a stable mass of live cells (often with encased holes or oscillators).

Class three CA known in detail include:

Rulestring Name Character Still lifes Oscillators Spaceships Orderly infinite growth patterns
B2/S Seeds Active no yes yes yes
(guns, puffers, rakes)
B2/S0 Live Free or Die Active yes (dot) yes yes yes
(guns, puffers, rakes)
B3/S023 DotLife Active yes yes yes yes
B37/S23 DryLife Active yes yes yes yes
B34/S34 34 Life Active yes (block) yes yes  ?
B35678/S5678 Diamoeba Stable no yes yes yes
(wickstretchers)
B3/S012345678 Life without death Stable yes no no yes
(ladders)

Some others with established names:

Rulestring Name Character
B234/S Serviettes Active
B3/S1234 Mazectric Stable
B3/S12345 Maze Stable
B3/45678 Coral Stable

See also