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Communications in Mathematical Physics

, Volume 306, Issue 2, pp 365–380 | Cite as

Rapid Convergence to Frequency for Substitution Tilings of the Plane

  • José Aliste-Prieto
  • Daniel Coronel
  • Jean-Marc Gambaudo
Article

Abstract

This paper concerns self-similar tilings of the Euclidean plane. We consider the number of occurrences of a given tile in any domain bounded by a Jordan curve. For a large class of self-similar tilings, including many well-known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan curve.

Keywords

Jordan Curve Substitution Matrix Substitution Rule Dilation Factor Primitive Substitution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • José Aliste-Prieto
    • 1
  • Daniel Coronel
    • 2
  • Jean-Marc Gambaudo
    • 3
  1. 1.Centro de Modelamiento MatemáticoUniversidad de ChileSantiagoChile
  2. 2.Facultad de MatemáticasPontificia Universidad Católica de ChileSantiagoChile
  3. 3.Laboratoire J.-A. DieudonnéUniversité de Nice - Sophia Antipolis, CNRSNice Cedex 02France

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