Search of Complex Binary Cellular Automata Using Behavioral Metrics

Abstract

We propose the characterization of binary cellular automata using a set of behavioral metrics that are applied to the minimal Boolean form of a cellular automaton's transition function. These behavioral metrics are formulated to satisfy heuristic criteria derived from elementary cellular automata. Behaviors characterized through these metrics are growth, decrease, chaoticity, and stability. From these metrics, two measures of global behavior are calculated: 1) a static measure that considers all possible input patterns and counts the occurrence of the proposed metrics in the truth table of the minimal Boolean form of the automaton; 2) a dynamic measure, corresponding to the mean of the behavioral metrics in $n$ executions of the automaton, starting from $n$ random initial states. We use these measures to characterize a cellular automaton and guide a genetic search algorithm, which selects cellular automata similar to the Game of Life. Using this method, we found an extensive set of complex binary cellular automata with interesting properties, including self-replication.