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On the Structure of Ammann A2 Tilings

  • Bruno Durand
  • Alexander Shen
  • Nikolay VereshchaginEmail author
Article
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Abstract

We establish a structure theorem for the family of Ammann A2 tilings of the plane. Using that theorem we show that every Ammann A2 tiling is self-similar in the sense of Solomyak (Discret Comput Geom 20:265–279, 1998). By the same techniques we show that Ammann A2 tilings are not robust in the sense of Durand et al. (J Comput Syst Sci 78(3):731–764, 2012).

Keywords

Ammann tilings Non-periodic tilings Self-similar tilings Substitution tilings Robust tilings 

Notes

Acknowledgements

We are sincerely grateful to G. Varouchas, M. Raskin and to anonymous referees for helpful remarks. We thank A. Korotin for a careful reading a preliminary version of the text, which helped to improve essentially the exposition.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.LIRMMUniversité de Montpellier IIMontpellierFrance
  2. 2.Moscow State University and National Research University Higher School of EconomicsMoscowRussian Federation

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