Anisotropy in cellular automata

Time-dependent and stationary patterns produced by standard cellular automata used for various qualitative modeling purposes show various geometric features that reflect the anisotropy of the underlying grid and neighborhood rather than the properties of the physical model itself. We investigate several modifications of cellular automata such as random grids, stochastic local functions, asynchronous evaluations that are designed to avoid anisotropy. We apply these tools to a class of simple totalistic automata simulating contact processes. It appears that random grids are most useful.