Complex Dynamics Behaviors in Cellular Automata Rule 35
Qi Han, Xiaofeng Liao, Chuandong Li and Liping Feng
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 στ-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 ε1/19 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.
Keywords: cellular automata (ca), bernoulli shift, topological entropy, symbolic dynamics