Universality classes of chaotic cellular automata

Abstract

Cellular automata (CA) are discrete, spatially-homogeneous, locally-interacting dynamical systems of very simple construction, but which exhibit a rich intrinsic behavior. Even starting from disordered initial configurations, CA can evolve into ordered states with complex structures crystallized in space-time patterns. In this paper we concentrate on deterministic one-dimensional CA defined by rules that lead to chaotic patterns. In order to find universality classes for these rules we associate a growth process with the CA dynamics and study the temporal behavior of the growth exponent, skewness and kurtosis of the height distribution of the interface. We obtain four universality classes characterized by different values of the growth exponent. These are related to the random deposition and directed percolation classes.