Interval Maps and Cellular Automata

Abstract

We associate to cellular automata elementary rules a class of interval maps defined in [0,1]. The considered configuration space is the space of the one-sided sequences in the set {0,1} and with the appropriate choice of the update procedure the interval maps do not depend on the boundary conditions. We study the rule 184 and obtain a family of transition matrices that characterizes the dynamics of the cellular automaton. We show that these matrices can be obtained recursively by an algorithm that depends on the local rule.