It was discovered only fairly recently that there is a pair of tiles with which the entire plane can only be tessellated in a non-periodic way. These tiles are very simple, but have remarkably surprising and deep mathematical properties, as well as giving beautiful tessellations.

References:

1. Austin, D Penrose tiles
2. Penrose, R 1989 Tilings and quasicrystals: a nonlocal growth problem? pages 53-80 in Introduction to the Mathematics of Quasicrystals, edited by Marko Jaric, Academic Press.

Supervisor: Professor Stephen Huggett