Cellular automata and nonlinear dynamical models (Q578915)

A point of view is pursued in which cellular automata (CA) are viewed as a laboratory to investigate nonlinear dynamics. We introduce an irreversible cellular automaton (ICA) with minimal coupling which exhibit class 4 behavior. Periodic structures (phases) are studied along with their stability properties. We observe topological conserved quantities and introduce a classification of structures via a topological number. Time reversal invariant cellular automata (TRCA) are also investigated; we discuss stability of phases and use a concept of local entropy to measure the growth of chaos in slightly perturbed phases. A classification of approach to chaos into 3 classes is proposed for TRCA.