Relationships between cellular automata model parameters and their physical counterparts

When constructing a Cellular Automata (CA) model of a natural process one meets a problem of determining scaling relations, i.e. the quantitative relationships between the CA dimensionless parameters and corresponding values characterizing the prototype process given in terms of a physical system of units. The problem has no general solution. Moreover, till now there is no strict statement and detailed investigation of the problem despite the fact that for some classes of CA models certain approaches have been proposed. The most formalized and substantiated approach is based on the similitude theory, which studies dimensionless characteristics of natural processes that are equal both for a model and its prototype. Certain attempts have been made to use the approach when developing and investigating particular CA models of natural phenomena, but no systematic methods have been created. In this paper the problem is discussed, and basic principles of finding scaling relations are formulated and shown at work for two most advanced classes of CA models: Lattice-Gas CA simulating viscous flows and stochastic CA models of Reaction-Diffusion processes.