Complex Symbolic Dynamics of One Class of Cellular Automata Rules

Changbing Tang, F. Chen, Weifeng Jin
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Abstract

In this paper, the dynamical behaviors of elementary cellular automata (ECA) rule 35 are studied from the viewpoint of symbolic dynamics. It is proved that rule 35, a member of Wolfram’s class II, possesses rich and complicated dynamical behaviors in its two subsystems; that is, rule 35 is topologically mixing and possesses the positive topological entropy on each subsystem. Meanwhile, the phenomena of collisions provide an intriguing and valuable bridge for proving that the union of these two subsystems is not the global attractor. Finally, it is noted that the method presented in this work is also applicable to studying the dynamics of other ECA rules, especially the 112 Bernoulli-shift rules therein.
一类元胞自动机规则的复杂符号动力学
本文从符号动力学的角度研究了初等元胞自动机(ECA)规则35的动力学行为。证明了规则35作为Wolfram II类的一员,在其两个子系统中具有丰富而复杂的动力学行为;也就是说,规则35是拓扑混合的,并且在每个子系统上具有正拓扑熵。同时,碰撞现象为证明这两个子系统的并并不是全局吸引子提供了一个有趣而有价值的桥梁。最后指出,本文提出的方法也适用于研究其他ECA规则的动力学,特别是其中的112条伯努利移位规则。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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