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Prevalence of Odometers in Cellular Automata

Ethan M. Coven·Marcus Pivato·Reem Yassawi·.
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Abstract

We consider a left permutive cellular automaton Phi, with no memory and positive anticipation, defined on the space of all doubly infinite sequences with entries from a finite alphabet. For each such automaton that is not one-to-one, there is a dense set of points X (which is large in another sense too) such that the Phi-orbit closure of each x in X is topologically conjugate to an odometer (the ``+1'' map on a projective limit of finite cyclic groups). We identify this odometer in several cases.

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Ethan M. Coven, Marcus Pivato, Reem Yassawi, .. 2005-11-01. Prevalence of Odometers in Cellular Automata. https://arxiv.org/abs/math/0511030

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