## Infinite Number of Chaotic Generalized Sub-shifts of Cellular Automaton Rule 180

### BibTeX

@MISC{Chen_infinitenumber,

author = {Wei Chen and Fangyue Chen and Yunfeng Bian and Jing Chen},

title = {Infinite Number of Chaotic Generalized Sub-shifts of Cellular Automaton Rule 180},

year = {}

}

### OpenURL

### Abstract

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.

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