Why Penrose Tiles Never Repeat

The first 200 people to get 20% off an annual premium subscription to Brilliant. Thanks to Brilliant for their support. This video is about a better way to understand Penrose tilings (the famous tilings invented by Roger Penrose that never repeat themselves but still have some kind of order/pattern). This project was a collaboration with Aatish Bhatia (). REFERENCES Explore Penrose and Penrose-like patterns: Video by Derek Muller/Veritasium about Penrose Patterns: Music algorithmically generated, algorithm designed by Henry Reich N.G. de Bruijn’s paper introducing the pentagrid/Penrose idea: De Bruijn, N.G., 1981. Algebraic theory of Penrose’s non-periodic tilings of the plane. Kon. Nederl. Akad. Wetensch. Proc. Ser. A, 43(84), . Here are some excellent in-depth references on how to construct Penrose Tiles Using the Pentagrid Method: Penrose Tilings Tied up in Ribbons by David Austin: The Empire Problem in Penrose Tilings by Laura Effinger-Dean: ~bailey/ Pentagrids and Penrose Tilings by Stacy Mowry & Shriya Shukla: &Shukla_Pentagrids and Penrose Tiling by Andrejs Treibergs: ~treiberg/ Algebraic Theory of Penrose’s Non-Periodic Tilings of the Plane by N. G. de Bruijn: Particularly good and helpful, and (we think) an undergrad thesis which is impressive!: ~bailey/ An interesting popular science read on the discovery on quasicrystals and their connection to Penrose Tilings: The Second Kind of Impossible by Paul Steinhardt: Support MinutePhysics on Patreon! Link to Patreon Supporters: MinutePhysics is on twitter - @minutephysics And facebook - Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! Created by Henry Reich