**Islamic geometrical pattern.**

In Islamic art we find very mathematical ways of designing geometrical patterns. The gigantic mosaics are made to represent an infinite pattern which can go beyond the visible world. That can explain why the designers had to find ways of constructing patterns which could have complex ways of repeating themselves. The Egyptians where advanced on mathematics. We also know that during the Islamic golden age, ancient texts on Greek and Hellenistic mathematics as well as Indian mathematics were translated into Arabic.

We can find in these designs very advanced mathematical rules to create such big designs without any errors, especially for building that are 800 years old. Surprisingly, I have found great similarities with the Penrose Tiling named after mathematician and physicist Roger Penrose in the 1970s. Their are different sorts of ways to compose a what we call “aperdiodic tiling” pattern. Aperiodic tiling by it’s definition “can **only** tile the plane in a non-repeating manner. This is in contrast to non-periodic tiling that can tile the plane in an irregular manner but can **also** do so in a regular, periodic fashion.”

Here is a very good explanation of different sets of aperiodic tilling: http://grahamshawcross.com/2012/10/12/aperiodic-tiling/

I also found this interesting article that speaks about research on ancient Islamic Penrose tiling: here

Other ressources:

Here is a very good encyclopedia of wonderful mathematical tilings.

On my page of Tools to create and explore computer generated patterns you can find some programs to generate Penrose tilings.

A few links for mathematical textile/