International Symposium on Nonlinear Theory and its Applications
Symbolic Dynamics of Some Bernoulli-shift Cellular Automata Rules
Guanrong Chen, Fangyue Chen, Junbiao Guan, Weifeng Jin,
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In our recent study, the dynamics of some elementary cellular automata rules are investigated in the biinfinite symbolic sequence space. These rules, as members of the Wolfram class II and Chua’s topologically-distinct Bernoulli-shift rules, which were believed to be simply periodic before, actually display rich and complex dynamics. Rules 2 and 35, for example, to be discussed in this paper, are chaotic in the sense of Li-Yorke and/or Devaney; they are topologically transitive or topologically mixing; they have positive topological entropies; and they show a catalog of gliders and glider collisions.