Cellular automata diffusion models for multicomputer implementation

Simulating large-scale phenomena by Cellular Automata (CA) meets the problem of designing CA models that could be efficiently implemented on supercomputers with distributed memory. Since most of large-scale spatially distributed processes contain diffusion as a component which takes a significant part of computational time, the study of coarse-grain parallelization characteristics of CA diffusion are of interest. There is a scope of investigations of CA diffusion models and their modifications. Most of them concern a two-dimensional case, although in large-scale simulation tasks three-dimensional processes are under investigation. Moreover, the known information on CA diffusion is incomplete and scattered among different scientific journals. In this paper, all known data are systematized and supplemented with parameters of three-dimensional CA diffusion. Three parameters of the model are considered to be most important for developing large-scale simulation algorithms: diffusion number of the model, the number of interprocessor exchanges in parallel implementation, and the computational time. Based on the given data analysis some recommendations are made how to make a proper choice of the CA diffusion model.