Self-Similarity of Persian TOND Patterns, Through the Logic of the X-Tiles
  • Jean-Marc CasteraEmail author
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Looking at the heritage of traditional Persian pentagonal patterns (patterns made from tiles derived from the pentagon), one can suppose that the artists, very early on, have set targets for their creation. One is the search for self-similarity; another is the search for methods of connection between the two main families of patterns. It is strange and intriguing that the historic artists did not fully achieve these targets.

This paper, following a previous publication (Castera, Nexus Netw J 18:223, 2016), proposes solutions and new developments.

There are no Penrose patterns in that story; only binary tiling and the X-Tiles.


Persian pentagonal patterns Multilevel patterns X-Tiles Self-similarity Binary tiling 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Independent ArtistParisFrance

Section editors and affiliations

  • Bharath Sriraman
    • 1
  • Kyeong-Hwa Lee
    • 2
  1. 1.Department of Mathematical SciencesThe University of MontanaMissoulaUSA
  2. 2.Department of Mathematics Education, College of EducationSeoul National UniversitySeoulSouth Korea

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