B3 Non-refereed article in a conference publication
Pattern Generation by Cellular Automata (Invited Talk)
Authors: Kari Jarkko
Editors: Femke van Raamsdonk
Publication year: 2013
Book title : 24th International Conference on Rewriting Techniques and Applications (RTA 2013)
Series title: LIPIcs
First page : 1
Last page: 3
Number of pages: 3
ISBN: 978-3-939897-53-8
ISSN: 1868-8969
DOI: https://doi.org/10.4230/LIPIcs.RTA.2013.1
Web address : http://drops.dagstuhl.de/opus/volltexte/2013/4049/
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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