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Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow

Jan Baetens (UGent) and Bernard De Baets (UGent)
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Abstract
Leaving a few exceptions aside, cellular automata (CA) and the intimately related coupled-map lattices (CML), commonly known as continuous cellular automata (CCA), as well as models that are based upon one of these paradigms, employ a regular tessellation of an Euclidean space in spite of the various drawbacks this kind of tessellation entails such as its inability to cover surfaces with an intricate geometry, or the anisotropy it causes in the simulation results. Recently, a CCA-based model describing steady-state heat flow has been proposed as an alternative to Laplace's equation that is, among other things, commonly used to describe this process, yet, also this model suffers from the aforementioned drawbacks since it is based on the classical CCA paradigm. To overcome these problems, we first conceive CCA on irregular tessellations of an Euclidean space after which we show how the presented approach allows a straightforward simulation of steady-state heat flow on surfaces with an intricate geometry, and, as such, constitutes an full-fledged alternative for the commonly used and easy-to-implement finite difference method, and the more intricate finite element method.
Keywords
cellular automata, finite element analysis, finite difference methods, heat transfer

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Chicago
Baetens, Jan, and Bernard De Baets. 2010. “Continuous Cellular Automata on Irregular Tessellations : Mimicking Steady-state Heat Flow.” In 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC 2011), 53–59. Piscataway, NJ, USA: IEEE.
APA
Baetens, Jan, & De Baets, B. (2010). Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow. 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC 2011) (pp. 53–59). Presented at the 2010 2nd World congress on Nature and Biologically Inspired Computing (NaBIC 2010), Piscataway, NJ, USA: IEEE.
Vancouver
1.
Baetens J, De Baets B. Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow. 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC 2011). Piscataway, NJ, USA: IEEE; 2010. p. 53–9.
MLA
Baetens, Jan, and Bernard De Baets. “Continuous Cellular Automata on Irregular Tessellations : Mimicking Steady-state Heat Flow.” 2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC 2011). Piscataway, NJ, USA: IEEE, 2010. 53–59. Print.
@inproceedings{1234600,
  abstract     = {Leaving a few exceptions aside, cellular automata (CA) and the intimately related coupled-map lattices (CML), commonly known as continuous cellular automata (CCA),  as well as models that are based upon one of these paradigms, employ a regular tessellation of an Euclidean space in spite of the various drawbacks this kind of tessellation entails such as its inability to cover surfaces with an intricate geometry, or the anisotropy it causes in the simulation results. Recently, a CCA-based model describing steady-state heat flow has been proposed as an alternative to Laplace's equation that is, among other things, commonly used to describe this process, yet, also this model suffers from the aforementioned drawbacks since it is based on the classical CCA paradigm. To overcome these  problems, we  first conceive CCA on irregular tessellations of an Euclidean space after which we show how the presented approach allows a straightforward simulation of steady-state heat flow on surfaces with an intricate geometry, and, as such, constitutes an full-fledged alternative for the commonly used and easy-to-implement finite difference method, and the more intricate finite element method.},
  author       = {Baetens, Jan and De Baets, Bernard},
  booktitle    = {2010 Second World Congress on Nature and Biologically Inspired Computing (NaBIC 2011)},
  isbn         = {9781424473779},
  keyword      = {cellular automata,finite element analysis,finite difference methods,heat transfer},
  language     = {eng},
  location     = {Fukuoka, Japan},
  pages        = {53--59},
  publisher    = {IEEE},
  title        = {Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow},
  url          = {http://dx.doi.org/10.1109/NABIC.2010.5716301},
  year         = {2010},
}

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