Geometric patterns in islamic art

This was in the news recently so you might have seen it...

Physics student Peter J. Lu has discovered, after his trip to Uzbekistan, that the geometric patterns shown on the walls of old islamic shrines depicted a very complex mathematical pattern, one that was only found in the west during last century.

I feel the article at ScienceNews.org explains it all very well, and shows plenty of pictures of the patterns AND of the underlying tilings, plus has references and links for further study, so I'll just refer you there:

Ancient Islamic Penrose Tiles