Soliton-like behavior in automata

Abstract

We propose a new kind of automaton that uses newly computed site values as soon as they are available. We call them Filter Automata (FA); they are analogous to Infinite Impulse Response (IIR) digital filters, whereas the usual Cellular Automata (CA) correspond to Finite Impulse Response (FIR) digital filters. It is shown that as a class the FA's are equivalent to CA's, in the sense that the same array of space-generation values can be produced; they must be generated in a different order, however. A particular class of irreversible, totalistic FA's are described that support a profusion of persistent structures that move at different speeds, and these particle-like patterns collide in nondestructive ways. They often pass through one another with nothing more than a phase jump, much like the solitons that arise in the solution of certain nonlinear differential equations. Histograms of speed, displacement, and period are given for neighborhood radii from 2 to 6 and particles with generators up to 16 bits wide. We then present statistics, for neighborhood radii 2 to 9, which show that collisions which preserve the identity of particles are very common.