in medieval architecture, signs of noncommutative geometry?

MOSAIC SOPHISTICATION A quasi-crystalline Penrose pattern at the Darb-i Imam shrine in Isfahan, Iran

A few days ago I noticed this article in NYT science section that reports on a recent paper by Lu and Steinhardt in Science (see here and here for the full article; thanks to `thomas1111'). Their abstract says: ``The conventional view holds that girih (geometric star-and-polygon, or strapwork) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, where the lines were drafted directly with a straightedge and a compass. We show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons ("girih tiles") decorated with lines. These tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly perfect quasi-crystalline Penrose patterns, five centuries before their discovery in the West''.

Interestingly enough the occurrence of quasi periodic tilings in old Persian art was also extensively commented on, last year, in Alain and Matilde's article ``A walk in the noncommutative garden" (see Section 9 on tilings). The first four pics are from their article. (see also lieven le bruyn’s weblog where the NYT article is commented at). We look forward to comments by people in NCG, operator algebras, and those working on quasi periodic crystals.