The Structure of the Elementary Cellular Automata Rule Space

Abstract

Abstract. The structure of th e elementary cellular automata rule space is investigated. The probabiliti es for a rule to be connected to other rules in th e same class (intra-class) , as well as rules in different classes (inter-class), are determined. The intr a-class connection prob abilities vary from around 0.3 to 0.5, an indication of th e strong tendency for rules with the similar behavior to be next to each other. Rules are also group ed according to th e mean-field descriptions. The mean-field clusters are classified into three classes (nonlinear, linear, and inversely linear) according to the "hot bit s " in the rule table. It is shown that such classification provides another easy way to describe the rule space. 1.