The concept of invariants in reaction-diffusion cellular automata

A concept of invariants in the cellular automata (CA) models is introduced, being defined as a dimensionless value that characterizes the process simulated by a CA evolution irrespective of the form of its mathematical representation. This paper is concerned with asynchronous CA-models (ACA-models), simulating reaction-diffusion processes, although it may be expanded to synchronous case as well. Invariants associate the CA-model parameters with their physical counterparts, which is important in simulation of real life processes. Particularly, the invariants may be used for obtaining the scaling values for space and time. The invariants of some simple reaction-diffusion ACA-models are established and considered in detail.