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.
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References
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I strongly recommend also the reading of every publication from Antony Lee, Peter Cromwell (available on https://girih.wordpress.com/), Emil Makovicky and Craig Kaplan
With a special mention to the recent brilliant work of the French mathematician Armand Jaspar, available on line: http://patterns-islamiques.fr/
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Castera, JM. (2019). TOND to TOND. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_58-2
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DOI: https://doi.org/10.1007/978-3-319-70658-0_58-2
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