Cellular Automata composition techniques for spatial dynamics simulation

A Cellular Automaton (CA) is nowadays an object of ever growing interest as a mathematical model for spatial dynamics simulation. Due to the CA ability to simulate nonlinear and discontinuous processes, it is expected to become a complement to partial differential equations. Particularly, the CA may be helpful when there is no other mathematical model of a phenomenon to be simulated. The fact is, there is no formal procedure to construct a CA-model according to a given qualitative or a quantitative specification of a space-time process. But, there exists a relatively large bank of CA that may be used for constructing the new complex CA models out of several known simple ones. In order to exploit this possibility CA composition methods are needed. The main purpose of this paper is to present a theoretical foundation and its basis on CA composition techniques in a generalized and systematic form. To capture all features of a great diversity of CA-models, a more general formalism for CA-algorithms representation, namely, Parallel Substitution Algorithm is chosen as a mathematical tool. The paper combines the results about the subject under consideration that are scattered in publications, most of them being original.