Girih, 20th of April 2012.

mosque, girih, red

My coleague and friend >> Primož Ziherl drew my attention a couple of months ago to the paper "Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture" published in Science, 315, 1106 (2007). The paper was written by Peter J. Lu and Paul J. Steinhardt, and it puts forth the idea that the Persian decorators around the year 1450 (and perhaps even two hundred years earlier) learned to tile the plane aperiodically, with a symmetry that is quite similar to quasi-crystalline >> Penrose tiling.

Namely, an important part of the decoration of mosques and Islamic shrines are the so called girih patterns which are a tightly woven network with a strict mathematical symmetry (girih means knot in Persian). Lu and Steinhardt, on the basis of analysis of patterns on shrines and mosques, claim that the decorators basically discovered aperiodic plane tiling, quite similar to the one discovered by Penrose. It is perhaps seen the best on the walls of Darb-e Imam shrine in Iran. >> Wikipedia's page about girih patterns has a lot of information and I suggest it as a starting point for all those that are interested in the story.

This page of the "Construction of Reality" deals with my short "study" of the Penrose tiling and its visualization on the structure similar to a mosque. The first variant of that shrine is shown in the image above. Note the girih patterns on the walls and the tiles of the floor. These tiles aperiodically tile the regular decagon.

mosque, girih, red, view from above

When we look at the floor tiles from above (the image above), we see that the floor tiling has a pentagonal central symmetry. It is a very typical form of Penrose tiling.

It is perhaps interesting to compare this shrine and its decagonal (pentagonal) symmetry with the octagonal symmetry of the >> Leonardo's temple, which I constructed on the basis of Leonardo da Vinci's sketches.

mosque, girih, red, detail

The detail of girih on the walls of the mosque is shown in the image above, and the image below shows the detail of the floor tiling. This tiling can be made with only two types of (triangular) tiles. Those two types were "made" out of two different kinds of stone.

mosque, tiling, detail

Of course, as I already wrote the automatized code for girih, I couldn't resist trying some other patterns. The image below shows one of such variations.

mosque, girih, blue

A detail of, this time blue, girih is shown in the image below.

mosque, girih, detail, blue

A third variant of the mosque is shown in the image below. The decorations were made differently this time and one could hardly call it a girih. But the mathematics is, of course, the same.

mosque, plates with patterns

A detail of the wall decoration is shown in the image below.

mosque, detail of the wall decoration

One could say that this is another in the series of posts on the plane tilings. Previous posts can be seen at:


In the next post, in about a week, I will shortly describe how I constructed the Penrose tiling. Until then!

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Last updated: 20th of April 2012.