Clewlow, Les (1989) Cellular automata and dynamical systems. PhD thesis, University of Warwick.

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Abstract

In this thesis we investigate the theoretical nature of the mathematical structures
termed cellular automata.
Chapter 1: Reviews the origin and history of cellular automata in order to place the
current work into context.
Chapter 2: Develops a cellular automata framework which contains the main
aspects of cellular automata structure which have appeared in the literature. We present a
scheme for specifying the cellular automata rules for this general model and present six
examples of cellular automata within the model.
Chapter 3: Here we develop a statistical mechanical model of cellular automata
behaviour. We consider the relationship between variations within the model and their
relationship to dynamical systems. We obtain results on the variance of the state changes,
scaling of the cellular automata lattice, the equivalence of noise, spatial mixing of the lattice
states and entropy, synchronous and asynchronous cellular automata and the
equivalence of the rule probability and the time step of a discrete approximation to a
dynamical system.
Chapter 4: This contains an empirical comparison of cellular automata within our
general framework and the statistical mechanical model. We obtain results on the transition
from limit cycle to limit point behaviour as the rule probabilities are decreased. We
also discuss failures of the statistical mechanical model due to failure of the assumptions
behind it.
Chapter 5: Here a practical application of the preceding work to population genetics
is presented. We study this in the context of some established population models and
show it may be most useful in the field of epidemiology. Further generalisations of the
statistical mechanical and cellular automata models allow the modelling of more complex
population models and mobile populations of organisms.
Chapter 6: Reviews the results obtained in the context of the open questions introduced
in Chapter 1. We also consider further questions this work raises and make some
general comments on how these may apply to related fields.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Cellular automata, Dynamics
Official Date:	November 1989
Dates:	Date Event November 1989 Submitted
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Thesis Type:	PhD
Publication Status:	Unpublished
Sponsors:	Science and Engineering Research Council (Great Britain) (SERC)
Extent:	106 leaves
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/4233

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