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.
By Cruz Godar
By Jonathan Love
By Robert Corless
By Sébastien Labbé
By Ian Short
By Bernat Espigule
By Vlerë Mehmeti
By Karl-Mikael Perfekt
