Brian Blackmore with Cyrus Taylor

Period and Periodicity of Classes of Cellular Automata

Cellular automata (CA), or lattice systems coupled with local rules, can be used to model a variety of dynamical systems including neural networks, chaotic systems, biological systems, and gas lattice systems.  CA have a variety of physically-realizable properties such as dissipation, reversibility, and periodicity, all of which are poorly explained by current theories.

     Periodicity of CA will be examined, starting with W-Rule systems, in an attempt to quantify periodicity and a period-to-parameter relationship for the W-Rule.  Generalization will proceed to arbitrary states, neighborhood sizes, and lattice sizes.  Generalized periodic CA will then be examined in an attempt to find reduced rule sets encapsulating large numbers of periodic rules for a given cellular space.