License: 
Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
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://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/4049/
Kari, Jarkko
Pattern Generation by Cellular Automata (Invited Talk)
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}
}
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Keywords: |
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cellular automata, pattern generation, Z-numbers |
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Collection: |
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24th International Conference on Rewriting Techniques and Applications (RTA 2013) |
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Issue Date: |
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2013 |
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Date of publication: |
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24.06.2013 |
