Islamic geometrical pattern

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.

56104-large 56105-large 56118-large 56123-large 56245-large 56260-large Mekhnes_Place_El-Hedine_Mosaique2 Tassellatura_alhambra

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:

Girih tiles

Aperiodic Tiling1Tile-coloured Aperiodic_tiling_with_3_tiles Binary_patch_03 Frett_K_B_03 Golden_Rhomboid_Triangle petra_2_gr_1 robinson_patch_03

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/

http://lib.fo.am/mathematickal_arts_2011

http://delta.fo.am/re-touches

http://www.toroidalsnark.net/mathknit.html

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