COARSE-GRAINING INVARIANT PATTERNS OF ONE-DIMENSIONAL TWO-STATE LINEAR CELLULAR AUTOMATA

Abstract

We consider one-dimensional two state cellular automata and their orbital patterns. We are particulary interested in initial states and their orbital pattern which are invariant under a certain coarse-graining operation. We show that invariant initial states are automatic. Moreover, we numerically study the complex nature of the initial states and their invariant orbits.