The non-repeating tile pattern

aperiodic tiling

Mathematicians have created a 13-sided tile shape that produces a pattern that never repeats.

A shape that produces a non-repeating pattern is known as an einstein (German for 'one stone'), although this shape has been nicknamed 'the hat'.

Mathematicians have been searching for such a shape for decades. It was not even clear if it could exist. But, with the help of a lot of computing power, the shape has been found along with a proof that it is aperiodic, as a not repeating pattern is called. And the shape is a lot simpler than many had supposed it would need to be.

In fact, there have been two proofs, one itself including new maths, which, according to The Times newspaper, has already led to the discovery of another aperiodic shape that is said to look a bit like a turtle. And there could be a whole family of other geometrically linked einstein shapes. 

It is probably only a matter of time before a tile company manufactures tiles in an einstein shape, although laying them is not as straightforward as laying rectangles and, as the pattern does not repeat, any template would need to be as big as the wall or floor being tiled.

If such a tile is ever to be used on a wall or floor, it will certainly test the skills and the patience of the tiler(s) laying it.