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
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.
Keywords
- cellular automata
- pattern generation
- Z-numbers
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