Five tiles and a thousand years of Persian walls

Stand in front of a fourteenth-century Timurid wall and the pattern seems to have no beginning. It does. There are five of them.

The five tiles

Craftsmen across Persia, Anatolia and Central Asia worked with a small, fixed set of shapes — a regular decagon, a regular pentagon, an elongated hexagon, a bowtie and a rhombus. Every one of them carries the same strapwork lines across its edges, drawn at the same angle, so that when two tiles meet the straps continue across the join without a seam.

The part most people miss

What you see on the finished wall is the strapwork. The tiles themselves are invisible — they are scaffolding, and they get plastered over.

This is why the patterns feel like they could go on forever: they can. The tiling is aperiodic in places, and a famous 2007 paper in Science argued that some fifteenth-century examples anticipate mathematics not formally described in the West until the 1970s. That claim has been debated since, which is worth saying — but the construction method is not in doubt.

Drawing one

You need a compass, a straight edge, and the patience to divide a circle into ten. The rest is repetition. We put thirty of these constructions, in numbered steps, in Draw Geometric Patterns, each one followed by a blank grid so you can do it immediately rather than three chapters later.