Embedding odometers in cellular automata

Volume 206 / 2009

Ethan M. Coven, Reem Yassawi 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.”

Authors

  • Ethan M. CovenDepartment of Mathematics
    Wesleyan University
    Middletown, CT 06457-0128, U.S.A.
    e-mail
  • Reem YassawiDepartment of Mathematics
    Trent University
    Peterborough, ON, Canada K9L 1Z8
    e-mail

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