aequationes mathematicae

, Volume 53, Issue 1–2, pp 295–307 | Cite as

Fractal Penrose tilings I. Construction and matching rules

  • C. Bandt
  • P. Gummelt
Research Papers


Quasiperiodic tilings of kite-and-dart type, widely used as models for quasicrystals with decagonal symmetry, are constructed by means of somewhat artificial matching rules for the tiles. The proof of aperiodicity uses a self-similarity property, or inflation procedure, which requires drawing auxiliary lines. We introduce a modification of the kite-and-dart tilings which comes very naturally with both properties: the tiles are strictly self-similar, and their fractal boundaries provide perfect matching rules.

AMS subject classification

Primary 52C20 Secondary 28A80 


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Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • C. Bandt
    • 1
  • P. Gummelt
    • 1
  1. 1.FB Mathematik und InformatikArndt-UniversitätGreifswaldGermany

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