Temporally Stochastic Cellular Automata: Classes and Dynamics

Abstract

This article introduces temporally stochastic cellular automata where a cell of the cellular system can be updated using one of the two elementary cellular automata rules, say [Formula: see text] and [Formula: see text]. The [Formula: see text] is the default rule and [Formula: see text] is temporally applied to the overall system with some probability that acts as noise to the system. As the mathematical analysis of such system is a difficult task, we use qualitative and quantitative simulations to study the dynamics of these temporally stochastic cellular automata. We are specially interested to exploring if it is possible that two periodic (resp. chaotic) rules together depict chaotic (resp. periodic) dynamics. To answer these questions, we fully classify temporally stochastic cellular automata. The study further observes phase transition and various types of class transition in the temporally stochastic cellular automata.