Generation of porous media computer representation by two-layer totalistic cellular automaton
Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 120-128.

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In the paper, two-layer totalistic cellular automaton allowing to generate porous materials computer representation is presented. Two-layer cellular automaton is constructed as a parallel composition of a totalistic cellular automaton and an asynchronous cellular automaton. The second layer gives an opportunity to form complex inhomogeneous structures similar to a patterns emerging in natural phenomena. The investigation aims to create a method for porous media morphology synthesis according to a given set of properties such as porosity, percolation, density, etc. Two-layer totalistic cellular automaton allows to obtain a set of patterns representing different porous media morphology. In addition, a porous medium characteristics such as percolation degree, porosity, the number of connected components are calculated and can be used for the analysis and selection of materials with necessary morphology.
Keywords: totalistic cellular automaton, parallel composition of cellular automata, activator, inhibitor, porous media, stable patterns.
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A. E. Kireeva. Generation of porous media computer representation by two-layer totalistic cellular automaton. Prikladnaâ diskretnaâ matematika, no. 1 (2015), pp. 120-128. http://geodesic.mathdoc.fr/item/PDM_2015_1_a12/

[1] Bandman O. L., “Using Cellular Automata for porous media simulation”, J. Supercomputing, 57:2 (2011), 121–131 | DOI

[2] Bandman O. L., “Metod postroenija kletochno-avtomatnyh modelej processov formirovanija ustojchivyh struktur”, Prikladnaya Diskretnaya Matematika, 2010, no. 4, 91–99 (in Russian)

[3] Chua L. O., Hasler M., Moschytz G. S., and Neirynck J., “Autonomous cellular neural networks: A unified paradigm for pattern formation and active wave propagation”, IEEE Trans. Circuits and Systems, 42 (1995), 559–577 | DOI | MR

[4] Young D. A., “A local activator-inhibitor model of vertebrate skin patterns”, Math. Biosciences, 72 (1984), 51–58 | DOI | MR

[5] Turing A. M., “The chemical basis of morphogenesis”, Philosophical Transactions of the Royal Society of London. Ser. B. Biol. Sci., 237:641 (1952), 37–72 | DOI

[6] Gierer A., Meinhardt H., “A theory of biological pattern formation”, Kybernetik, 12:1 (1972), 30–39 | DOI

[7] Gierer A., “Generation of biological patterns and form: Some physical, mathematical and logical aspects”, Progress in Biophysics and Molecular Biology, 37 (1981), 1–47 | DOI | MR

[8] Bandman O. L., “Kletochno-avtomatnye modeli prostranstvennoj dinamiki”, Sistemnaja Informatika. Metody i Modeli Sovremennogo Programmirovaniya, 2006, no. 10, 59–113 (in Russian)

[9] Bandman O. L., “Cellular Automata composition techniques for spatial dynamics simulation”, Bulletin of the Novosibirsk Computing Center. Ser. Comp. Sci., 27 (2008), 1–39 | Zbl

[10] Chopard B., Droz M., Cellular Automata Modeling of Physical Systems, Cambridge University Press, 1998, 337 pp. | MR | Zbl