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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York (1996)
Inverso, S., Kunkle, D., Merrigan, C.: Evolutionary Methods for 2-D Cellular Automata Computation (2002), http://www.cs.rit.edu/~drk4633/mypapers/gacaProj.pdf
Mitchell, M., Crutchfield, J.P.: The Evolution of Emergent Computation. Proceedings of the National Academy of Sciences, SFI Technical Report 94-03-012
Mitchell, M., Crutchfield, J.P., Hraber, P.T.: Evolving cellular automata to perform computations: Mechanisms and impediments. Physica D 75, 361–391 (1994)
Li, W., Packard, N.H., Langton, C.G.: Transition phenomena in cellular automata rule space. Physica D 45, 77–94 (1990)
Wolfram, S.: Statistical mechanics of Cellular Automata. Reviews of Modern Physics, vol. 55 (1983)
Wolfram, S.: Theory and Applications of Cellular Automata. World Scientific, Singapore (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Breukelaar, R., Bäck, T. (2004). Evolving Transition Rules for Multi Dimensional Cellular Automata. In: Sloot, P.M.A., Chopard, B., Hoekstra, A.G. (eds) Cellular Automata. ACRI 2004. Lecture Notes in Computer Science, vol 3305. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30479-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-30479-1_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23596-5
Online ISBN: 978-3-540-30479-1
eBook Packages: Springer Book Archive