A minimal subsystem of the Kari-Culik tilings

Jason Siefken

doi:10.1017/etds.2015.118

A minimal subsystem of the Kari-Culik tilings

Jason Siefken^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-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 language	English (US)
Pages (from-to)	1607-1634
Number of pages	28
Journal	Ergodic Theory and Dynamical Systems
Volume	37
Issue number	5
DOIs	https://doi.org/10.1017/etds.2015.118
State	Published - Aug 1 2017

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/etds.2015.118

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A minimal subsystem of the Kari-Culik tilings

Abstract

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