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The Q-toothpick Cellular Automaton
Stockholms universitet.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
2019 (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
Old City Publishing, 2019. Vol. 14, no 1-2, p. 51-68
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-71816ISI: 000462875500003OAI: oai:DiVA.org:kau-71816DiVA, id: diva2:1304100
Available from: 2019-04-11 Created: 2019-04-11 Last updated: 2019-04-11Bibliographically approved

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Mossberg, Eva

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