Directed percolation phenomena in asynchronous elementary cellular automata

Abstract

Cellular automata are discrete dynamical systems that are widely used to model natural systems. Classically they are run with perfect synchrony; i.e., the local rule is applied to each cell at each time step. A possible modification of the updating scheme consists in applying the rule with a fixed probability, called the synchrony rate. It has been shown in a previous work that varying the synchrony rate continuously could produce a discontinuity in the behaviour of the cellular automaton. This works aims at investigating the nature of this change of behaviour using intensive numerical simulations. We apply a two-step protocol to show that the phenomenon is a phase transition whose critical exponents are in good agreement with the predicted values of directed percolation. © Springer-Verlag Berlin Heidelberg 2006.