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The Ammann–Beenker Tilings Revisited

  • Nicolas Bédaride
  • Thomas FerniqueEmail author

Abstract

This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all be seen as digitization of two-dimensional planes in the four-dimensional Euclidean space. This family contains the Ammann–Beenker tilings as the solution of a simple optimization problem.

Notes

Acknowledgements

We thank T.Q.T. Le for sending us the preprint [8] which inspired the proof of Lemma 8.1, and the referee, notably for pointing us the highly relevant reference [5] (see below).

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.LATPUniv. Aix-MarseilleMarseilleFrance
  2. 2.LIPNCNRS & Univ. Paris 13ParisFrance

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