Gliders, Collisions and Chaos of Cellular Automata Rule 62

摘要

This paper provides a systematic analysis of glider dynamics and interactions in rule 62, including a catalog of glider collisions. Based on these empirical observations, it is proved that rule 62 defines a subsystem with complicated dynamical properties in the bi-infinite symbolic sequence space, such as topologically mixing and positive topological entropy. Meanwhile, the phenomena of glider collisions provide an intriguing and valuable bridge for researching the symbolic dynamics of rule 62 in the bi-infinite case, especially for proving that the union of period-3 attractor and Bernoulli attractors is not the global attractor.