islamic star tile3 In Medieval and Renaissance European art much emphasis was placed on representational techniques including, of course, perspective. We’ll be looking at some of the maths behind perspective in a workshop course in the new year.In the Islamic world, however, a somewhat different path was followed. In possession of Euclidean geometry, its artisans used straightedge-and-compass techniques to construct abstract patterns of considerable intricacy. These are very simple but once you have some basic skills with them they offer a huge number of possibilities (while also ruling out others).To learn about the classical Islamic approach to pattern-making have a look at this resource from the V&A or this one from the Met Museum. Both give some ideas for exploration using the most basic kit imaginable — a compass, something straight, a sharp pencil and a big sheet of paper.

Tiling patterns, though, get a little weirder than this. In the 1970s Roger Penrose discovered and investigated ways to tile a floor in such a way that, no matter how big the floor and how small the tiles, the pattern will never repeat exactly. These are called aperiodic tilings and you can read a bit about them here, here and here.

A big surprise came when, in 2007, Peter Lu showed that Penrose tilings may have already been known to Islamic craftsmen in the fifteenth century.

A tiling can be thought of as a systematic scheme for dividing up space: it makes sense to speak of tilings of three-dimensional space, or even space of higher dimensions. There are also some puzzles to be solved about tiling surfaces that aren’t flat, such as the inside of a dome. We’ll look at some of these topics in the course “Strange Spaces” in 2015.