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Cellular automata on irregular tessellations

Jan Baetens (UGent) and Bernard De Baets (UGent)
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Abstract
To this day, most articles on cellular automata (CA) employ regular tessellations of R-n, notwithstanding this kind of tessellation suffers from a few serious drawbacks limiting the appraisal of regular CA as full-fledged modelling tools. In this article, we propose an extension to the classical CA paradigm, by allowing irregular tessellations of R-n, which, in essence, encloses the regular tessellations as a special case. After a short review on the major shortcomings of CA on regular tessellations, we establish a definition for CA on irregular tessellations of R-n that is followed by a profound elaboration of its constituents. In addition, we propose a graph representation that is applicable to an important family of irregular CA, and, in accordance with the framework developed for CA on regular tessellations, we present an enumeration scheme for the k-state, theta-sum irregular (outer-)totalistic CA. Illustrative examples conclude this article.
Keywords
discrete dynamical systems, cellular automata, enumeration, formalism, irregular tessellations, MODEL, SIMULATION, DYNAMICS, FIRE, RAINFALL, WILDFIRE, NETWORK, SYSTEMS, GROWTH, GAME

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MLA
Baetens, Jan, and Bernard De Baets. “Cellular Automata on Irregular Tessellations.” DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, vol. 27, no. 4, 2012, pp. 411–30, doi:10.1080/14689367.2012.711300.
APA
Baetens, J., & De Baets, B. (2012). Cellular automata on irregular tessellations. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 27(4), 411–430. https://doi.org/10.1080/14689367.2012.711300
Chicago author-date
Baetens, Jan, and Bernard De Baets. 2012. “Cellular Automata on Irregular Tessellations.” DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL 27 (4): 411–30. https://doi.org/10.1080/14689367.2012.711300.
Chicago author-date (all authors)
Baetens, Jan, and Bernard De Baets. 2012. “Cellular Automata on Irregular Tessellations.” DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL 27 (4): 411–430. doi:10.1080/14689367.2012.711300.
Vancouver
1.
Baetens J, De Baets B. Cellular automata on irregular tessellations. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL. 2012;27(4):411–30.
IEEE
[1]
J. Baetens and B. De Baets, “Cellular automata on irregular tessellations,” DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, vol. 27, no. 4, pp. 411–430, 2012.
@article{3220345,
  abstract     = {{To this day, most articles on cellular automata (CA) employ regular tessellations of R-n, notwithstanding this kind of tessellation suffers from a few serious drawbacks limiting the appraisal of regular CA as full-fledged modelling tools. In this article, we propose an extension to the classical CA paradigm, by allowing irregular tessellations of R-n, which, in essence, encloses the regular tessellations as a special case. After a short review on the major shortcomings of CA on regular tessellations, we establish a definition for CA on irregular tessellations of R-n that is followed by a profound elaboration of its constituents. In addition, we propose a graph representation that is applicable to an important family of irregular CA, and, in accordance with the framework developed for CA on regular tessellations, we present an enumeration scheme for the k-state, theta-sum irregular (outer-)totalistic CA. Illustrative examples conclude this article.}},
  author       = {{Baetens, Jan and De Baets, Bernard}},
  issn         = {{1468-9367}},
  journal      = {{DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL}},
  keywords     = {{discrete dynamical systems,cellular automata,enumeration,formalism,irregular tessellations,MODEL,SIMULATION,DYNAMICS,FIRE,RAINFALL,WILDFIRE,NETWORK,SYSTEMS,GROWTH,GAME}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{411--430}},
  title        = {{Cellular automata on irregular tessellations}},
  url          = {{http://doi.org/10.1080/14689367.2012.711300}},
  volume       = {{27}},
  year         = {{2012}},
}

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