PARTICLE-LIKE STRUCTURES AND THEIR INTERACTIONS IN SPATIOTEMPORAL PATTERNS GENERATED BY ONE-DIMENSIONAL DETERMINISTIC CELLULAR-AUTOMATON RULES

Configurations generated by the evolution of some one-dimensional cellular automata may be viewed, after many time steps, as particlelike structures evolving in a regular background. A classification of the most frequently observed "particles" is proposed according to their specific behavior. The simplest-a straightforward generalization of the "kinks" in range-1 Rule 18 earlier studied by Grassberger [Phys. Rev. A 28, 3666 (1983)]-exhibit a diffusive motion and annihilate according to simple processes. Others have, in contrast, constant (positive, negative, or zero) velocities. The "collision" of particles with different velocities leads to some "reactions" in which some particles are annihilated and others are created. A detailed description of such "reactions" sheds new light on the large-time behavior of range-1 rule 54 with a very slow decrease of the particle number, as t-gamma (gamma congruent-to 0.15). More "exotic" behaviors are sometimes observed. Some particlelike structures radiate other "particles." Some "particles" combine to generate a perturbation whose space extension increases with time and can be annihilated through the interactions with other "particles." These different behaviors could lead to a more precise classification of cellular-automation rules.