Designing a collision matrix for a cellular automaton with rest particles for simulation of wave processes

We consider the single-particle HPPrp Lattice Gas Cellular Automata for simulation of modeling wave processes. The HPPrp Cellular Automaton is defined on a two-dimensional square lattice. Each cell of the automaton contains particles of the two types: the moving particles and the rest particles. Inserting the rest particles leads to non-deterministic collision rules. In this paper, the design of a procedure collision matrix for a cellular automaton with rest particles for simulation wave processes is presented. The entries of the collision matrix are transition probabilities from one state to another. As the condition that ensures the existence of a wave process, the semi-detailed balance condition is used.