science:

Usually, when art and science, or science and religion, intersect, they are seen as being in opposition. Art is free-flowing where science is rigorous; religion is faith-based where science needs evidence. But sometimes, the three actually intersect in ways that, at least to my eye, actually heighten the beauty of all of them. One such example is medieval Muslim ornamentation.

Imagine you have a fixed set of tile shapes, but you can have as many of each as you want. Can you tile them in such a way that you fill an infinite plane, with no gaps? If you can, you’ve got yourself a tiling. If you can shift the pattern around in some way, say, one unit to the left, so that the end result is the same as you started with, you’ve got a periodic tiling. But if any shift at all in the pattern creates a unique pattern, the tiling is said to be non-periodic. And if you’ve got a set of tile shapes that can only form non-periodic tilings, no matter what pattern you make with them, the set of tiles is said to be aperiodic. Until the mid-20th century, mathematicians doubted that there could be aperiodic tilings. But in the 1970s, Roger Penrose discovered a set of very simple tiles that—if you apply a couple of restrictions to how they can be arranged (restrictions that can be made superfluous if you give the tiles some bumps)—are aperiodic, i.e., no matter how you arrange these tiles, and no matter how large a plane you tile, you will never find a periodic pattern. They’re called Penrose tiles.

This was new knowledge. No one knew about this until Western mathematics started exploring this in the mid-20th century. Or so we thought.

Because of Islam’s restrictions on religious iconography, such as depicting living beings, Islamic artists have found ways to make the most of abstract patterns and shapes. You see it in Arabic calligraphy, and you see it in the magnificent shapes on the walls of mosques and religious schools. In 2007, physicists Peter Lu and Paul Steinhardt discovered that the patterns on the walls of medieval Islamic buildings very closely resemble Penrose tilings. The crucial invention of girih tiles, basic shapes used to build more complex patterns, allowed Islamic architects to decorate their walls with non-periodic tilings. And in the Darb-e Imam shrine in Ishafan, Iran, built around 1450 (above), the tiles almost perfectly form a pattern that can be generalized as a Penrose tiling. If you deconstruct the pattern on the Darb-e Imam shrine into Penrose tiles, you’ll find that only 11 out of 3700 are mismatched, and the mismatch is so small that it’s “removable with a local rearrangement of a few tiles without affecting the rest of the pattern”. (more)