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A minimal subsystem of the Kari–Culik tilings

Published online by Cambridge University Press:  11 February 2016

JASON SIEFKEN
JASON SIEFKEN*
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA email siefkenj@math.northwestern.edu
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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 $\mathbb{Z}^{2}$ 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 $m\times n$ configurations.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 5 , August 2017 , pp. 1607 - 1634
Copyright
© Cambridge University Press, 2016 

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