Embedding odometers in cellular automata
Volume 206 / 2009
Fundamenta Mathematicae 206 (2009), 131-138
MSC: Primary 37B10, 37B15
DOI: 10.4064/fm206-0-8
Abstract
We consider the problem of embedding odometers in one-dimensional cellular automata. We show that (1) every odometer can be embedded in a gliders-with-reflecting-walls cellular automaton, which one depending on the odometer, and (2) an odometer can be embedded in a cellular automaton with local rule $x_i \mapsto x_i + x_{i+1} \bmod n$ ($i \in \mathbb Z$), where $n$ depends on the odometer, if and only if it is “finitary.”
