On the effect of topology on cellular automata rule spaces

Warne, David (2013) On the effect of topology on cellular automata rule spaces. (Unpublished)

Abstract

This thesis presents an empirical study of the effects of topology on cellular automata rule spaces. The classical definition of a cellular automaton is restricted to that of a regular lattice, often with periodic boundary conditions. This definition is extended to allow for arbitrary topologies. The dynamics of cellular automata within the triangular tessellation were analysed when transformed to 2-manifolds of topological genus 0, genus 1 and genus 2.

Cellular automata dynamics were analysed from a statistical mechanics perspective. The sample sizes required to obtain accurate entropy calculations were determined by an entropy error analysis which observed the error in the computed entropy against increasing sample sizes. Each cellular automata rule space was sampled repeatedly and the selected cellular automata were simulated over many thousands of trials for each topology. This resulted in an entropy distribution for each rule space.

The computed entropy distributions are indicative of the cellular automata dynamical class distribution. Through the comparison of these dynamical class distributions using the E-statistic, it was identified that such topological changes cause these distributions to alter. This is a significant result which implies that both global structure and local dynamics play a important role in defining long term behaviour of cellular automata.

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ID Code: 76202
Item Type: Other
Refereed: No
Keywords: Graph Cellular Automata, Critical Phenomena, Discrete Dynamical Systems, Topology, 2-Manifold
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Pure Mathematics not elsewhere classified (010199)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > MATHEMATICAL PHYSICS (010500) > Mathematical Physics not elsewhere classified (010599)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100) > Simulation and Modelling (080110)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Analysis of Algorithms and Complexity (080201)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200) > Computation Theory and Mathematics not elsewhere classified (080299)
Divisions: Current > Schools > School of Electrical Engineering & Computer Science
Current > Research Centres > High Performance Computing and Research Support
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 16 Sep 2014 23:58
Last Modified: 18 Sep 2014 08:02

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