Geometric & Functional Analysis GAFA

, Volume 6, Issue 3, pp 471–488 | Cite as

The construction of self-similar tilings

  • R. Kenyon
Article

Abstract

We give a construction of a self-similar tiling of the plane with any prescribed expansion coefficient λɛℂ (satisfying the necessary algebraic condition of being a complex Perron number).

For any integerm>1 we show that there exists a self-similar tiling with 2π/m-rotational symmetry group and expansion λ if and only if either λ or λe2π∿/m is a complex Perron number for which e2π∿/m is in ℚ[λ], respectivelyQe2πı/m].

Keywords

Expansion Coefficient Symmetry Group Algebraic Condition Perron Number Prescribe Expansion 

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Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • R. Kenyon
    • 1
  1. 1.CNRS UMR 128 Ecole Normale Supérieure de LyonLyonFrance

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