TOND to TOND
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.
KeywordsPersian pentagonal patterns Multilevel patterns X-Tiles Self-similarity Binary tiling
- Binary tilling: http://www.quadibloc.com/math/pen02.htm
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- With a special mention to the recent brilliant work of the French mathematician Armand Jaspar, available on line: http://patterns-islamiques.fr/