About

Repeat Unit is a notebook about tilings: how shapes fill a plane, why some do and some do not, and how to find the small piece a pattern is built from.

The notes are written slowly and for my own understanding first, so expect them to be corrected and extended over time. Proofs are sketched rather than complete; where something is a well-known result, the name of the person who proved it is there so it can be looked up.

Every diagram on this site is drawn by a small script from a handful of numbers: lattice vectors, a random seed, the length of a segment. Nothing is traced from photographs.

Floors, walls and old paving are the best source of new questions. If a pattern looks simple but you cannot say what its repeat unit is, it is probably worth a note.