Evolution of cellular automata using instruction-based approach

Abstract

This paper introduces a method of encoding cellular automata local transition function using an instruction-based approach and their design by means of genetic algorithms. The proposed method represents an indirect mapping between the input combinations of states in the cellular neighborhood and the next states of the cells during the development steps. In this case the local transition function is described by a program (algorithm) whose execution calculates the next cell states. The objective of the program-based representation is to reduce the length of the chromosome in case of the evolutionary design of cellular automata. It will be shown that the instruction-based development allows us to design complex cellular automata with higher success rate than the conventional table-based method especially for complex cellular automata with more than two cell states. The case studies include the replication problem and the problem of development of a given pattern from an initial seed.