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Weak local rules for planar octagonal tilings

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Abstract

We provide an effective characterization of the planar octagonal tilings which admit weak local rules. As a corollary, we show that they are all based on quadratic irrationalities, as conjectured by Thang Le in the 1990s.

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Authors and Affiliations

  1. Institut de Mathématiques de Marseille, Aix-Marseille Université, Technopôle Château-Gombert, 39 rue Frédéric Joliot-Curie, 13453, Marseille Cedex 13, France

    Nicolas Bédaride

  2. Laboratoire d’Informatique de Paris Nord, Université Paris 13, 99 avenue Jean-Baptiste Clément, 93430, Villetaneuse, France

    Thomas Fernique

Authors
  1. Nicolas Bédaride
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  2. Thomas Fernique
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Corresponding author

Correspondence to Nicolas Bédaride.

Additional information

This work was supported by the ANR project QuasiCool (ANR-12-JS02-011-01).

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Bédaride, N., Fernique, T. Weak local rules for planar octagonal tilings. Isr. J. Math. 222, 63–89 (2017). https://doi.org/10.1007/s11856-017-1582-z

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  • DOI: https://doi.org/10.1007/s11856-017-1582-z

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