Diffusion processes occur in many scientific areas, they are especially important in chemistry, biology and medicine. The most part of mathematical models for a description of diffusion are nonlinear Partial Differential Equations which do not have analytical solutions, and numerical methods require large computing resources. As scientific interest to the structures (fractal clusters) generated in the result of diffusion processes grows, the search of new models is intensified. The important method complementary to mathematical models is imitation modeling in which space mobility of the particles of a substance is directly modeled.
There are two directions in such an approach: an imitation of random walks of particles and cellular automata modeling. In this work we implement based on random walk algorithms for the modeling of the growth of fractal clusters on triangulated surfaces. We use classical variants of Diffusion Limited Aggregation (DLA) and Reaction Limited Aggregation (RLA) models. It is shown that for Cluster Cluster Aggregation (CCA) model fractal cluster cannot be constructed correctly without additional assumptions about the cluster restructuring.
The software is implemented on Python language and may be used by both researchers and students as a tool for modeling complex processes.