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The Q-toothpick Cellular Automaton
Stockholm University, Faculty of Science, Department of Physics.
Number of Authors: 22019 (English)In: Journal of Cellular Automata, ISSN 1557-5969, Vol. 14, no 1-2, p. 51-68Article in journal (Refereed) Published
Abstract [en]

In a toothpick-type cellular automaton, a shape is drawn, and then at each time-step copies of the same shape are attached at certain predetermined places. The resulting pattern exhibits unexpected growth properties. We investigate the fractal-like large-scale behavior of the Q-toothpick cellular automaton, which is built from quarter circles, with starting configurations consisting of an arbitrary number of quarter circles. In this paper, we prove that infinitely long barriers of quarter circles arise in the pattern, and divide it into non-interacting triangular parts. Furthermore, we show that the behavior of these triangular parts is described by the one-dimensional elementary cellular automaton rule 18 and is related to the Sierpinski triangle.

Place, publisher, year, edition, pages
2019. Vol. 14, no 1-2, p. 51-68
Keywords [en]
Toothpick cellular automaton, Large-scale behavior, Fractal, Sierpinski triangle, Rule 18, Rule 90
National Category
Computer and Information Sciences Mathematics Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-168471ISI: 000462875500003OAI: oai:DiVA.org:su-168471DiVA, id: diva2:1313126
Available from: 2019-05-02 Created: 2019-05-02 Last updated: 2019-05-02Bibliographically approved

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