The Complexity of Permutive Cellular Automata

This paper studies cellular automata in two aspects: Ergodic and topological behavior. For ergodic aspect, the formulae of measure-theoretic entropy, topological entropy and topological pressure are given in closed forms and Parry measure is demonstrated to be an equilibrium measure for some potential function. For topological aspect, an example is examined to show that the exhibition of snap-back repellers for a cellular automaton infers Li-Yorke chaos. In addition, bipermutive cellular automata are optimized for the exhibition of snap-back repellers in permutive cellular automata whenever two-sided shift space is considered.