A minimal subsystem of the Kari-Culik tilings

Jason Siefken*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The Kari-Culik tilings are formed from a set of 13 Wang tiles that tile the plane only aperiodically. They are the smallest known set of Wang tiles to do so and are not as well understood as other examples of aperiodic Wang tiles. We show that the action by translation on a certain subset of the Kari-Culik tilings, namely those whose rows can be interpreted as Sturmian sequences (rotation sequences), is minimal. We give a characterization of this space as a skew product as well as explicit bounds on the waiting time between occurrences of configurations.

Original languageEnglish (US)
Pages (from-to)1607-1634
Number of pages28
JournalErgodic Theory and Dynamical Systems
Volume37
Issue number5
DOIs
StatePublished - Aug 1 2017

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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