To cellular automata models on triangulation grids
UDC
510.67:554DOI:
https://doi.org/10.31429/vestnik-15-2-5-11Abstract
The paper deals with cellular automata on triangulation grids, which allow modeling of three-dimensional processes on curvilinear surfaces in terms of cellular automata. This approach can serve as a basis for modeling various phenomena, not limited to diffusion processes. The results of computational modeling show that the realized cellular automata are not inferior qualitatively to CA on rectangular grids and at the same time allow modeling processes on surfaces of complex geometry.
The authors created an application that implements on the various surfaces the CA a model of naive diffusion that interprets the process as a chaotic movement of particles, resulting in an equalization of the impurity concentration in the introduced cellular space. There is a transition from Boolean values to continuous functions describing the impurity concentration field, produced by averaging over neighboring cells. The described approach can be generalized for constructing cellular automata on different curvilinear surfaces with a pronounced nonlinearity using an arbitrary triangulation grid. The obtained results can be applied to construct more complex composite CA, including the interpretation of several phenomena, among which diffusion is present.
Keywords:
cellular automata, triangulation, diffusion, curvilinear surfaceAcknowledgement
References
- von Neumann, J. The theory of self-reproducing automatas. Mir, Moscow, 1971. (In Russian)
- Toffoli, T. Cellular automata as an alternative to rather than approximation of differential equations in modeling physics. Physica D., 1984, vol. 10, pp. 117-127.
- Toffolli, T., Margolus, N. Cellular automata machines. MIT Press, USA, 1987.
- Bandman O. Comparative study of cellular automata diffusion models. Lecture Notes in Computer Science, 1999, vol. 1662, pp. 395-399.
- Weimar, J. Cellular automata for reaction-diffusion systems. Parallel Computing, 1997, vol. 23, no. 11, pp. 1699-1715.
- Boccara N. Reaction-diffusion complex systems. Springer, Berlin, 2004.
- Bandman O. Parallel simulation of asynchronous cellular automata evolution. Proc. of 7th Int. Conf. on Cellular Automata, for Research and Industry (ACRI 2006), 2016, vol. 4173 of LNCS. Springer. pp. 41-47.
- Bandman O.L. A method for construction of cellular automata simulating pattern formation processes. Theoretical background of applied discrete mathematics, 2010, no. 4, pp. 91-99.
- Evseev A.A., Nechaeva O.I. Cellular automata modeling of diffusion processes on a triangulation grids. Prikladnaya diskretnaya matematika [Applied Discrete Mathematics]. 2009. no. 4, pp. 72-83. (In Russian)
- Bandman O.L. Cellular automata modeling of spatial dynamics. Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 2000. (In Russian)
- Rubtsov S.E., Pavlova A.V., Sunozov A.A. To cellular-automatic modeling of the process of diffusion and substances interaction. Zashhita okruzhajushhej sredy v neftegazovom komplekse [Environmental protection in the oil and gas sector], 2014, no. 2, pp. 30-34. (In Russian)
- Rubtsov S.E., Pavlova A.V., Savenkov S.I. About cellular-automatic models of convection-diffusion processes of substances. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2016, no. 4, pp. 62-68. (In Russian)
- Rubtsov S.E., Pavlova A.V. Cellular automata models of the fluid flow process in the presence of obstacles and impurities. Zashhita okruzhajushhej sredy v neftegazovom komplekse [Environmental protection in the oil and gas sector], 2016, no. 6, pp. 39-44. (In Russian)
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Copyright (c) 2018 Rubtsov S.E., Pavlova A.V., Rodionov P.R.
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