A survey of all state symmetric two state two dimensional cellular automata with rules based on cell counts using a Moore Neighbourhood in a torus universe. It finds three main classes of interesting behaviour, waves, crystals and chaos. Chaotic behaviour when the universe fills with ever changing patterns. Wave behaviour where the boundary between areas of different state supports complex waves. Crystallisation when the universe fills with unchanging patterns which often have low period oscillators trapped in them. In addition to minimal behaviour two small groups of rules show edge effects and the Structural properties. The edge effects are one dimensional oscillators on stable boundaries and the structural properties show up when the universe size has a major impact on the evolution of random patterns. The FredkinFredkin replicatorReplicator cellular automata being the sole member of the Structural category. Two interesting rules where discovered in which random islands either grow or shrink. In rule B34678/S3678Rule Rule smaller islands are more likely to shrink and larger ones expand. In rule B4/S01235678Rule Rule small holes in a random universe are more likely to shrink and larger ones expand.

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Waves, Crystals and Chaos a Survey of State Symmetric Cellular Automata

  • P. Rendell

摘要

A survey of all state symmetric two state two dimensional cellular automata with rules based on cell counts using a Moore Neighbourhood in a torus universe. It finds three main classes of interesting behaviour, waves, crystals and chaos. Chaotic behaviour when the universe fills with ever changing patterns. Wave behaviour where the boundary between areas of different state supports complex waves. Crystallisation when the universe fills with unchanging patterns which often have low period oscillators trapped in them. In addition to minimal behaviour two small groups of rules show edge effects and the Structural properties. The edge effects are one dimensional oscillators on stable boundaries and the structural properties show up when the universe size has a major impact on the evolution of random patterns. The FredkinFredkin replicatorReplicator cellular automata being the sole member of the Structural category. Two interesting rules where discovered in which random islands either grow or shrink. In rule B34678/S3678Rule Rule smaller islands are more likely to shrink and larger ones expand. In rule B4/S01235678Rule Rule small holes in a random universe are more likely to shrink and larger ones expand.