|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.