Introduction

The belief that complex macroscopic phenomena of everyday experience are consequences of cooperative effects and large-scale correlations among enormous numbers of primitive microscopic objects subject to short-range interactions, is the starting point of all mathematical models on which our interpretation of nature is based. The models used are basically of two types: continuous and discrete models.

The first have been until now the most current models of natural systems; their mathematical formulation in terms of differential equations allows analytic approaches that permit exact or approximate solutions. The power of these models can be appreciated if one thinks that complex macroscopic phenomena, such as phase transitions, approach to equilibrium and so on, can be explained in terms of them when infinite (thermodynamic) limits are taken.

More recently, the great development of numeric computation has shown that discrete models can also be good candidates to explain complex phenomena, especially those connected with irreversibility, such as chaos, evolution of macroscopic systems from disordered to more ordered states and, in general, self-organizing systems. As a consequence, the interest in discrete models has vastly increased. Among these, cellular automata, C.A. for short, have received particular attention; we recapitulate their definition:

A discrete lattice of sites, the situation of which is described at time t by integers whose values depend on those of the sites at the previous time t - τ (τ is a fixed finite time delay).