Chaos and gliders in periodic cellular automaton rule 62

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. © 2012 Old City Publishing, Inc.