|Thursday 2 July 2020|
|Events for day: Tuesday 27 November 2018|
| 14:00 - 15:00 Lecture|
Quantifying the Aperiodicity of a Wang Tile Set.
A (Wang) tile set is a finite set of unit squares where each edge got a color. A tile set T tiles the plane if the plane can be covered by Z^2-translated copies of elements of T, where two adjacent edges must have the same color. A tile set is aperiodic if it tiles the plane, but if this can not be done in a periodic way. Most aperiodic tilings are obtained from a substitution process (Penrose, Ammann-Beenker, Robinson,...). We will introduce two invariants to quantify the level of aperiodicity of a Wang tile set. The first one is topological, the second is metric. They both rely on the way a tile set til ...