Evolving Transition Rules for Multi Dimensional Cellular Automata

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.

Authors and Affiliations

1. Universiteit Leiden, LIACS, P.O. Box 9512, 2300 RA, Leiden, The Netherlands

   Ron Breukelaar & Thomas Bäck

2. Nutech Solutions GmbH, Martin-Schmeisser-Weg, 44227, Dortmund, Germany

   Thomas Bäck

Editors and Affiliations

1. Faculty of Sciences, Section of Computational Science, University of Amsterdam, Kruislaan 403, 1098 SJ, Amsterdam, The Netherlands

   Peter M. A. Sloot

2. Computer Science Department, University of Geneva, Switzerland

   Bastien Chopard

3. Section Computational Science, University of Amsterdam, The Netherlands

   Alfons G. Hoekstra

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