Islamic star patterns arose in the centuries after the birth of Islam, and spread quickly as Islamic rule grew outward from the Middle East to encompass western Europe, northern Africa, and southern Asia. This form of ornamentation peaked in the first half of the second millennium. The practice then tapered off as the borders of the Muslim world began to shrink. Today, historical artifacts can be found in countries from Spain to Uzbekistan, with important concentrations in Spain, Turkey, Iran, and Morocco.  
There is no precise definition of an Islamic star pattern, but there are some general trends. They tend to be rigidly geometric in design, and feature star-shaped polygonal regions. They can be found carved in wood or stone, built from latticework, or assembled from baked terracotta tiles...  
Although we have a large body of historical examples to study, we don't know exactly how artisans working at the time designed their star patterns. Their methods were typically guarded as trade secrets. Thus we are left with the exciting historical puzzle of reverse-engineering lost techniques, or inventing new ones altogether... I am interested in understanding how star patterns may have been designed in the first place, and how we can enlarge the space of designs using what we know today. I am also interested in how to render star patterns and how to manufacture them automatically from computer descriptions.
Site by Craig S. Kaplan (School of Computer Science, University of Waterloo) includes images of computer-generated patterns, along with examples of manufactured works.  
Also links to online (and downloadable) applications for creating your own star patterns, including the author's own Taprats.  
[cc: it's the arts]
Excellent find!
Laughing Muse: When I was growing up, I loved the Altair Design books. I haven't been able to find them again until recently, and I'm scanning the designs in so that I never lose them. This tells me more of the history behind the actual Islamic designs, and provides some software to create them myself. Excellent find!!! Thanks!!!!!