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Chaos and Gliders in Periodic Cellular Automaton Rule 62
Fangyue Chen, Lun Shi, Guanrong Chen and Weifeng Jin

In this paper, the dynamics of elementary cellular automaton rule 62 are investigated in the bi-infinite symbolic sequence space. Rule 62, a member of Wolfram’s class II and Chua’s robust period-3 rules, believed to be simply before, is shown to have rich and complex dynamics. It is proved that the global map of rule 62 defines a subsystem with complicated dynamical properties such as topologically mixing and positive topological entropy, and is thus chaotic in the sense of both Li-Yorke and Devaney. This work also provides a systematic analysis of glider dynamics and interactions in the evolution of the rule, including several natural gliders and a catalog of glider collisions, which were particularly studied in Wolfram’s complex rules 54 and 110.

Keywords: Cellular automata, glider, collision, symbolic dynamics, chaos.

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