A new class of automata networks

A new class of automata networks is defined. Their evolution rules are determined by a probability measure p on the set of all integers Z and an indicator function IA on the interval [0, 1]. It is shown that any cellular automaton rule can be represented by a (nonunique) rule formulated in terms of a pair (p, IA). This new class of automata networks contains discrete systems which are not cellular automata. For a given p, a metric can be defined on the space of all rules which induces a metric on the space of all cellular automata rules.