TOND to TOND: Self-Similarity of Persian TOND Patterns, Through the Logic of the X-Tiles

Jean-Marc Castera ()
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Jean-Marc Castera: Independent Artist

Chapter 27 in Handbook of the Mathematics of the Arts and Sciences, 2021, pp 801-839 from Springer

Abstract: Abstract 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.

Keywords: Persian pentagonal patterns; Multilevel patterns; X-Tiles; Self-similarity; Binary tiling (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/978-3-319-57072-3_58

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