Statistical analysis of Margolus's block-rotating mechanism cellular automation modeling the diffusion in a medium with discrete singularities

The generalization of Margolus’s block cellular automaton on a hexagonal grid is formulated. Statistical analysis of the results of probabilistic cellular automation for vast variety of this scheme solving the test task of diffusion is done. It is shown that the choice of the hexagon blocks is $25 \%$ more efficient than Y-blocks. It is shown that the algorithms have polynomial complexity, and the polynom degree lies within $\rm 0.6\div 0.8$ for parallel computer, and in the range $\rm 1.5\div 1.7$ for serial computer. The effects of embedded into automaton’s field defective cells on the rate of convergence are studied also.