Yes, the Turkmen gul format is not a quasicrystalline pattern, and any similarities could well be of a colollary nature. Interesting that this parallels Peter J. Lou's assertion that they are not sure of the nature of the relationship between the patterns and their underlying mathematics.There is a relationship, but what is it's nature? Did Islamic architects understand the math involved in their designs? This is the big question for Lou and Steinhardt.
Aside from general interest, my purpose in posting this article lies in the fact that I am pleased with the way it meshes with this "theory" of mine, which states that a large scale medallion, a star and line "girih" pattern, had it's origins in the early Islamic period. During the course of the expansion of the Islamic sphere, it seems to have been taken with them to those regions in which Islam took root, and to this day evident as an expression of artistic heratige.
The appearence of these more complex quasicrystaline patterns, derived from the "girih" pattern roughly correlates with the time frame in which the (believed) Turkmen rugs of the period moved from a more lattice oriented design, the Lotto rugs, to the more familiar (and constant) gul format.This also roughly coincides with the decline of the Timurids and the isolation of the Turkmen, resulting in stasis and the resulting constancy of the gul format. Ditto for the migration of the Turkmen to a more eastern location..
There are some similarities, between the quasicryastalline pattern and both gul and gul format, in that some guls seem composed of units roughly approximating these "girih tiles", and the grid like gul layout seems a rough approximation of a quasicrystalline pattern.But who can say, I don't presume to know for a fact that this is what transpired.
Now, Mr.Smith, there is an adage here in the States which makes reference to "the stove calling the kettle black',so please. I enjoyed my time at ****. I have been going through much change as of late and have been contentious at times, but nothing egregious. I realize that some of the parties here have been at odds, but I am not a partisan of this conflic, nor do I intend to be.