Accuracy and stability of spatial dynamics simulation by cellular automata evolution

Abstract

Accuracy and stability properties of fine-grained parallel computations, based on modeling spatial dynamics by cellular automata (CA) evolution, are studied. The problem arises when phenomena under simulation are represented as a composition of a CA and a function given in real numbers, and the whole computation process is transferred into a Boolean domain. To approach the problem accuracy of real spatial functions approximation by Boolean arrays, as well as of some operations on cellular arrays with different data types are determined and approximation errors are assessed. Some methods of providing admissible accuracy are proposed. Stability is shown to depend only of the nonlinear terms in hybrid methods, the use of CA-diffusion instead of Laplace operator having no effect on it. Some experimental results supporting the theoretical conclusions are presented. © Springer-Verlag Berlin Heidelberg 2003.