Generating Loop Patterns with a Genetic Algorithm and a Probabilistic Cellular Automata Rule

Abstract

The objective is to find a Cellular Automata (CA) rule that can generate “loop patterns”. A loop pattern is given by ones on a zero background showing loops. In order to find out how loop patterns can be locally defined, tentative loop patterns are generated by a genetic algorithm in a preliminary stage. A set of local matching tiles is designed and checked whether they can produce the aimed loop patterns by the genetic algorithm. After having approved a certain set of tiles, a probabilistic CA rule is designed in a methodical way. Templates are derived from the tiles, which then are used in the CA rule for matching. In order to drive the evolution to the desired patterns, noise is injected if the templates do not match or other constraints are not fulfilled. Simulations illustrate that loops and connected loops can be evolved by the CA rule.