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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.RTA.2013.1
URN: urn:nbn:de:0030-drops-40490
URL: http://drops.dagstuhl.de/opus/volltexte/2013/4049/
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Kari, Jarkko

Pattern Generation by Cellular Automata (Invited Talk)

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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.

BibTeX - Entry

@InProceedings{kari:LIPIcs:2013:4049,
  author =	{Jarkko Kari},
  title =	{{Pattern Generation by Cellular Automata (Invited Talk)}},
  booktitle =	{24th International Conference on Rewriting Techniques and Applications (RTA 2013)},
  pages =	{1--3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-53-8},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{21},
  editor =	{Femke van Raamsdonk},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4049},
  URN =		{urn:nbn:de:0030-drops-40490},
  doi =		{10.4230/LIPIcs.RTA.2013.1},
  annote =	{Keywords: cellular automata, pattern generation, Z-numbers}
}

Keywords: cellular automata, pattern generation, Z-numbers
Seminar: 24th International Conference on Rewriting Techniques and Applications (RTA 2013)
Issue Date: 2013
Date of publication: 14.06.2013


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