Geometry · a Light

A 1453 Isfahan shrine carries a pattern that never repeats

In 2007 Peter Lu and Paul Steinhardt published a paper in Science on the tilework of the Darb-i Imam shrine in Isfahan, finished in 1453. They showed that its patterns can be generated from a set of five decorated tiles, and that the result is close to a quasiperiodic tiling, a pattern with fivefold symmetry that never exactly repeats, of the kind Roger Penrose described in the 1970s and physicists later found in real crystals. What the paper did not claim is that the craftsmen had the modern concept. Emil Makovicky had described related patterns in a Maragha tomb in 1992, and other geometers disputed how much of the tiling is quasiperiodic. What is certain is that the geometry is on the wall.

Darb-i Imam, Isfahan · 1453