Evolving Transition Rules for Multi Dimensional Cellular Automata

Abstract

Abstract. Genetic Algorithms have been used before to evolve transition rules for one dimensional Cellular Automata (CA) to solve e.g. the majority problem and investigate communication processes within such CA [3]. In this paper, the principle is extended to multi dimensional CA, and it is demonstrated how the approach evolves transition rules for the two dimensional case with a von Neumann neighborhood. In particular, the method is applied to the binary AND and XOR problems by using the GA to optimize the corresponding rules. Moreover, it is shown how the approach can also be used for more general patterns, and therefore how it can serve as a method for calibrating and designing CA for real-world applications.

Using Genetic Algorithms to Evolve Behavior in Cellular Automata

“…In [3] this idea was extended to two dimensional CA and it was shown that two dimensional CA can match the performance of the one dimensional rules even though the neighborhood was two cells smaller. It was also shown that different kinds of problems can be solved using this approach (AND-, XORproblem and pattern generation) if it is extended to two dimensions.…”

“…If it is true that minimizing the distance in a CA will improve the performance of the CA then this might explain why multi dimensional CA seem to be more powerful than the one dimensional CA [3,2]. The topology of multi dimensional CA supports information travel in multiple directions and this decreases the distance between cells in the CA.…”

“…An experiment was conducted to compare different neighborhood shapes in combination with the well known Majority Problem (see Section 3) and measure what the impact of the different distance measures is on the performance. In order to test the performance of a neighborhood shape a GA was used to search for a good transition rule that solves the Majority Problem like was done in [2,3,4,14,15].…”

Discovery by Genetic Algorithm of Cellular Automata Rules for Pattern Reconstruction Task

“…The results produced by Mitchell et al were interesting and started development of a concept of automating rule generation using artificial evolution. Breukelaar and Back applied GAs [3] to solve the density classification problem as well as AND and XOR problem in two dimensional CAs. Swiecicka et al used [10] GAs to find CA rules able to solve multiprocessor scheduling problem.…”

Two-dimensional patterns and images reconstruction with use of cellular automata

“…It opened a possibility of automatic generation of CA rules using artificial evolution. In particular, in [2] GA was proposed to solve AND and XOR problem in 2D CA, and Bandini et al [1] proposed to use machine learning techniques to find CA rules able to generate patterns, which are similar to those generated by a given target rule.…”