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.
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