List of publications » Pattern Generation by Cellular Automata (Invited Talk)

B3 Article in conference proceedings

Pattern Generation by Cellular Automata (Invited Talk)

List of Authors: Jarkko Kari

Publication year: 2013

Book title *: 24th International Conference on Rewriting Techniques and Applications (RTA 2013)

Title of series: LIPIcs

Number of pages: 3

ISBN: 978-3-939897-53-8

ISSN: 1868-8969

Abstract

A one-dimensional cellular automaton is a discrete dynamical system where a sequence of symbols evolves synchronously according to a local update rule. We discuss simple update rules that make the automaton perform multiplications of numbers by a constant. If the constant and the number base are selected suitably the automaton becomes a universal pattern generator: all finite strings over its state alphabet appear from a finite seed. In particular we consider the automata that multiply by constants 3 and 3/2 in base 6. We discuss the connections of these automata to some difficult open questions in number theory, and we pose several further questions concerning pattern generation in cellular automata.

A one-dimensional cellular automaton is a discrete dynamical system where a sequence of symbols evolves synchronously according to a local update rule. We discuss simple update rules that make the automaton perform multiplications of numbers by a constant. If the constant and the number base are selected suitably the automaton becomes a universal pattern generator: all finite strings over its state alphabet appear from a finite seed. In particular we consider the automata that multiply by constants 3 and 3/2 in base 6. We discuss the connections of these automata to some difficult open questions in number theory, and we pose several further questions concerning pattern generation in cellular automata.

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