Periodic Patterns in Orbits of Certain Linear Cellular Automata

Abstract

We discuss certain linear cellular automata whose cells take values in a finite field. We investigate the periodic behavior of the verticals of an orbit of the cellular automaton and establish that there exists, depending on the characteristic of the field, a universal behavior for the evolution of periodic verticals.

Keywords

• cellular automata
• p-fold bifurcation of periods
• finite fields
• [info] computer science [cs]
• [info.info-cg] computer science [cs]/computational geometry [cs.cg]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]