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Complex dynamics behaviors in cellular automata rule 35. (English) Zbl 1236.37012
Summary: From the viewpoint of symbolic dynamics, the complex dynamical behaviors of rule 35 in cellular automata are investigated in this paper. Rule 35 which is Bernoulli $\sigma_\tau$-shift rule and is member of Wolfram’s class II, is said to be simple as periodic before. It is worthwhile studying dynamical behaviors of four rules, whether they possess chaotic attractors or not We find that rule 35 possess positive topological entropy, and is topologically mixing on its attractors. Therefore, dynamical behaviors of rule 35 are chaotic in the sense of both Li-York and Devaney. Then, we prove that four rules belonging to global equivalence $\varepsilon^1_{19}$ are topologically conjugate. Diagrams is used to explain the attractors of rule 35, where characteristic function is used to describe that some points fall into Bernoulli-shift map after several times iterations.
MSC:
37B15Cellular automata
37B10Symbolic dynamics
37B40Topological entropy