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Complex dynamics of cellular automata rule 119
Authors:Fang-Fang Chen
Institution:a Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, PR China
b School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang, 310018, PR China
Abstract:In this paper, the dynamical behaviors of cellular automata rule 119 are studied from the viewpoint of symbolic dynamics in the bi-infinite symbolic sequence space Σ2. It is shown that there exists one Bernoulli-measure global attractor of rule 119, which is also the nonwandering set of the rule. Moreover, it is demonstrated that rule 119 is topologically mixing on the global attractor and possesses the positive topological entropy. Therefore, rule 119 is chaotic in the sense of both Li-Yorke and Devaney on the global attractor. It is interesting that rule 119, a member of Wolfram’s class II which was said to be simple as periodic before, actually possesses a chaotic global attractor in Σ2. Finally, it is noted that the method presented in this work is also applicable to studying the dynamics of other rules, especially the 112 Bernoulli-shift rules therein.
Keywords:Cellular automata  Bernoulli _method=retrieve&  _eid=1-s2  0-S0378437108009928&  _mathId=si7  gif&  _pii=S0378437108009928&  _issn=03784371&  _acct=C000053510&  _version=1&  _userid=1524097&  md5=df835793b05bcbcd5afb3042a8be1760')" style="cursor:pointer  στ-Shift" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">στ-Shift  Symbolic dynamics  Attractor  Topological entropy  Transition matrix  Topologically mixing  Chaos
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