Ever heard of the Penrose tiling of the plane, the Rauzy fractal or the Kakutani sequence of partitions of the unit interval? In my talk I will introduce these beautiful geometric constructions, all of which are defined using simple substitution rules. We will inspect these substitution rules and see how matrices and graphs can be used to model them, and how powers of the matrices and paths on the graphs relate to tiles in the tilings and partitions of a set. These ideas and relations are simple but deep, and they will allow us to discover and prove some surprising properties of these well known constructions.

Pizza will be served.

Penrose tiling

Substitution partitions