Global Dynamics of Finite Cellular Automata

Authors:
Martin Schüle;Thomas Ott;Ruedi Stoop
Affiliations:
Institute of Neuroinformatics, ETH and University of Zurich, Zurich, Switzerland 8057;Institute of Applied Simulation, ZHAW Zurich, Wädenswil, Switzerland 8820;Institute of Neuroinformatics, ETH and University of Zurich, Zurich, Switzerland 8057
Venue:
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
Year:
2008

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Abstract

A novel algebraic and dynamic systems approach to finite elementary cellular automata is presented. In particular, simple algebraic expressions for the local rules of elementary cellular automata are deduced and the cellular automata configurations are represented via Fourier analysis. This allows for a further analysis of the global dynamics of cellular automata by the use of tools derived from functional analysis and dynamical system theory.