Complex Dynamics in Elementary Cellular Automaton Rule 26
Junbiao Guan and Fangyue Chen
The purpose of this paper is to explore complex dynamics in elementary cellular automaton rule 26. Firstly, we study the dynamics of this automaton through its interval map and its subsystem respectively. The positive topological entropy explored in its subsystem indicates that this automaton is topologically transitive on its subsystem. After that, we also study its shift representation under the framework of general symbolic dynamics. We show that rule 26 can be expressed by the shift on symbolic space with two symbols. The obtained results indicate that this automaton exhibits rich dynamical behavior.
Keywords: Elementary cellular automaton; rule 26; topological entropy; Bernoulli shift; symbolic dynamics.