Upper bound on the products of particle interactions in cellular automata

Particle-like objects are observed to propagate and interact in many spatia lly extended dynamical systems. For one of the simplest classes of such sys tems, one-dimensional cellular automata, we establish a rigorous upper boun d on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacti ng particles - a quantity which is defined here and which measures the amou nt of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidat ing why that approach is of general utility. The upper bound is tested agai nst several relatively complex domain-particle cellular automata and found to be tight. (C) 2001 Published by Elsevier Science B.V.