Pattern Generation by Cellular Automata (Invited Talk)

Author Jarkko Kari

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Jarkko Kari

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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)


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.
  • cellular automata
  • pattern generation
  • Z-numbers


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