Abstract — In this paper, the dynamics of elementary cellular automaton rule 41 is investigated in the bi-infinite symbolic sequence space. In spite of rule 41 is not surjective, but it possess of rich and complex dynamical behaviors. The existence of attractors and subshifts of finite type of the rule’s global map is strictly proved, some interesting dynamical properties on these subshifts, such as positive topological entropies, topological transitivity and topological mixing, chaos in the sense of Li-Yorke and Devaney, are revealed.

Abstract — This paper is devoted to an in-depth study of cellular automaton rule 180 under the framework of symbolic dynamics. Rule 180, a member of Wolfram’s class IV and Chua’s hyper Bernoulli shift rules, defines infinite number of generalized sub-shifts. An effective method of constructing the shift invariant sets of the rule’s global map is proposed. It is noted that this method is also applicable to studying the dynamics of other rules. Furthermore, the rich and complex dynamical behaviors on these sub-shifts, such as positive topological entropies, topologically mixing, and chaos in the sense of Li-Yorke and Devaney, are revealed.

Abstract — In this paper, the dynamics of elementary cellular automaton (ECA) rule 73 is investigated under the framework of the bi-infinite symbolic sequence space. This paper provides a rigorous mathematical analysis for the evolution of symbol sequences in some subsystems of rule 73. ECA rule 73, a member of Wolfram’s class III and Chua’s complex Bernoulli-shift rules, defines many more subsystems with rich and complicated dynamical properties such as topologically mixing, topologically transitivity and positive topological entropy, and henceforth the dynamical system generated by the global map of the rule is chaotic in the sense of both Devaney and Li-Yorke. Keywords: cellular automata; complex Bernoulli-shift CA rule; symbolic dynamics; topologically mixing; chaos. 1.

Complex dynamics emerging in Rule 30 with majority memory

1 Background and physical setup for road traffic 3 1.1 Historic origins of cellular automata 4 1.2 Ingredients of a cellular automaton 5 1.3 Road layout and the physical environment 7