Synchronous and Asynchronous Updating in Cellular Automata

Abstract

We analyze the properties of synchronous and various asynchronous methods to iterate cellular automata. Here we give just a brief summary of the results presented in [5]. Cellular automata are defined by a grid, a finite set of elementary states, a neighborhood and a local function which defines the dynamics. In classical cellular automata the local function is always applied synchronously to all the cells, i.e. they are evaluated and take their new values at the same moment. This corresponds to a discrete time scale. In analogy to a continuous time process the cells may also be evaluated and take their new states one after the other. We call this an asynchronous cellular automaton. Since this term has been used for quite different things in literature we would like to note that we do not mean a system like in [1] where the cells take their new values with a delay but are updated synchronously.