To cellular automata models on triangulation grids

Authors

  • Rubtsov S.E. Kuban State University, Krasnodar, Russian Federation
  • Pavlova A.V. Kuban State University, Krasnodar, Russian Federation
  • Rodionov P.R. Kuban State University, Krasnodar, Russian Federation

UDC

510.67:554

EDN

XRAFTV

DOI:

10.31429/vestnik-15-2-5-11

Abstract

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 surface

Funding information

Работа выполнена при поддержке гранта РФФИ и Администрации Краснодарского края 16-41-230175 р_а.

Authors info

  • Sergei E. Rubtsov

    канд. физ.-мат. наук, доцент кафедры математического моделирования Кубанского государственного университета

  • Alla V. Pavlova

    д-р физ.-мат. наук, профессор кафедры математического моделирования Кубанского государственного университета

  • Pavel R. Rodionov

    студент магистратуры кафедры математического моделирования Кубанского государственного университета

References

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Issue

Vol. 15 (2018) No. 2

Pages

5-11

Section

Mathematics

Dates

Submitted

June 6, 2018

Accepted

June 15, 2018

Published

June 27, 2018

How to Cite

[1]
Rubtsov, S.E., Pavlova, A.V., Rodionov, P.R., To cellular automata models on triangulation grids. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2018, т. 15, № 2, pp. 5–11. DOI: 10.31429/vestnik-15-2-5-11

License

Copyright (c) 2018 Рубцов С.Е., Павлова А.В., Родионов П.Р.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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