Apparaît dans la collection : 2026 - T1 - WS3 - Integrating Research and Illustration in Number Theory

De Bruijn proved in the early 1980's that Penrose aperiodic tilings can be constructed from a method based on multigrids. As observed by Moody and Lagarias in the 1990's, this method, now known as cut and project scheme, was originally formalized by Meyer in 1970's. A cut and project scheme includes a physical space (the space we want to tile) and an internal space (an additional helpful coordinate space).

Many known aperiodic tilings are 4-to-2 cut-and-project schemes, meaning that the dimension of both spaces is 2. These include Penrose tilings, the Ammann tilings, the Jeandel-Rao tilings and tilings by the hat monotile. The goal of this talk is to explain and understand aperiodic tilings coming from 4-to-2 cut and project schemes with illustrations, experimentations, discussions and using as many senses as possible (sight, hearing, touch, smell and taste) but mostly the first three.