Class three cellular automata: Difference between revisions
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'''Class three''' [[cellular automata]], according to the classification system of [[Stephen Wolfram]], are those where most patterns tend towards [[Chaos|chaotic]], seemingly infinite growth. They are thus the polar opposite of [[Class one cellular automata|class one]] CA. | {{Glossary}} | ||
'''Class three''' [[cellular automata]], according to the classification system of [[Stephen Wolfram]], are those where most patterns tend towards [[Chaos|chaotic]], seemingly infinite growth. They are thus the polar opposite of [[Class one cellular automata|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 cellular automata|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 [[Butterfly replicator|replicator]] means that sufficiently large patterns tend towards infinite growth. | 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 cellular automata|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 [[Butterfly replicator|replicator]] means that sufficiently large patterns tend towards infinite growth. | ||
Revision as of 09:39, 5 December 2014
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).
Type four 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 |