The spatial structure of odometers in certain cellular automata

Marcus Pivato (1) , Reem Yassawi (1)

1 Department of Mathematics

Recent work has shown that many cellular automata (CA) have configurations whose orbit closures are isomorphic to odometers. We investigate the geometry of the spacetime diagrams of these `odometer configurations'. For boolean linear CA, we exactly determine the positions of the consecutive `gears' of the odometer mechanism in the configuration. Then we characterize and explain the self-similar structure visible in the spacetime diagrams of odometer configurations for two classes of nonlinear CA: ratchet CA and Coven CA.

Domaines: Autre [cs.OH]

Marcus Pivato, Reem Yassawi. The spatial structure of odometers in certain cellular automata. JAC 2008, Apr 2008, Uzès, France. pp.119-129. ⟨hal-00273988⟩