Complex Symbolic Dynamics of One Class of Cellular Automata Rules

摘要

In this paper, the dynamical behaviors of elementary cellular automata (ECA) rule 35 are studied from the viewpoint of symbolic dynamics. It is proved that rule 35, a member of Wolfram's class II, possesses rich and complicated dynamical behaviors in its two subsystems; that is, rule 35 is topologically mixing and possesses the positive topological entropy on each subsystem. Meanwhile, the phenomena of collisions provide an intriguing and valuable bridge for proving that the union of these two subsystems is not the global attractor. Finally, it is noted that the method presented in this work is also applicable to studying the dynamics of other ECA rules, especially the 112 Bernoulli-shift rules therein.