On a Simple Stochastic Cellular Automaton with Avalanches: Simulation and Analytical Results

Abstract

Cellular automata (CA) models are widely used in many natural and human sciences. The rule that defines CA, which may be very simple, can lead to a very complicated evolution of a system and rich structure of produced patterns. It often comes from nonlinearity present in the system. The rule of the model encodes the crucial features of the phenomenon under investigation. It contains the information about the behaviour of the automaton and usually is suggestive (convincing) reference point for explanations of its properties. Instead of equations, the rule often plays a central role in description of automata. CA are also convenient and hence attractive tools for making computer simulations; being completely discrete, in principle, CA do not require any approximation procedure for machine implementation. © Springer-Verlag Berlin Heidelberg 2010.