Complex Systems

Parity Filter Automata Download PDF

Charles H. Goldberg
Department of Computer Science, Trenton State College,
Trenton, NJ 08625, USA


Parity filter automata are a class of two-state cellular automata on the integer grid points of the real line in which cells are updated serially from left to right in each time period rather than synchronously in parallel. Parity filter automata support large numbers of "particles," or persistent repeating configurations, and the collision of these particles is frequently a "soliton" collision in which the particles interact, but from which both emerge with their identities preserved. This paper presents a theory of such parity filter automata. Period and velocity theorems for particles, existence and uniqueness theorems, conservation and monotone nonconservation laws, duration and phase shifts in soliton collisions, and other results are proved.