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 (i ∈ ℤ), where n depends on the odometer, if and only if it is “finitary.”
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-8,
author = {Ethan M. Coven and Reem Yassawi},
title = {Embedding odometers in cellular automata},
journal = {Fundamenta Mathematicae},
volume = {205},
year = {2009},
pages = {131-138},
zbl = {1187.37017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-8}
}
Ethan M. Coven; Reem Yassawi. Embedding odometers in cellular automata. Fundamenta Mathematicae, Tome 205 (2009) pp. 131-138. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm206-0-8/