Embedding odometers in cellular automata

Coven, Ethan M. and Yassawi, Reem (2009). Embedding odometers in cellular automata. Fundamenta Mathematicae, 206 pp. 131–138.

DOI: https://doi.org/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 ↦ x_i + x_i+1 mod n (i ∈ ℤ), where n depends on the odometer, if and only if it is “finitary.”

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