LIPIcs.RTA.2013.1.pdf
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Pattern Generation by Cellular Automata (Invited Talk)
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24th International Conference on Rewriting Techniques and Applications (RTA 2013)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Rewriting Techniques and Applications (RTA) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2013-06-24
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Jarkko Kari. Pattern Generation by Cellular Automata (Invited Talk). In 24th International Conference on Rewriting Techniques and Applications (RTA 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 21, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.RTA.2013.1
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.
Subject Classification
Keywords
- cellular automata
- pattern generation
- Z-numbers
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