Why Penrose Tiles Never Repeat

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The first 200 people to https://brilliant.org/minutephysics 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 (https://aatishb.com). REFERENCES Explore Penrose and Penrose-like patterns: https://aatishb.com/patterncollider Video by Derek Muller/Veritasium about Penrose Patterns: https://www.youtube.com/watch?v=48sCx-wBs34 Music algorithmically generated, algorithm designed by Henry Reich N.G. de Bruijn’s paper introducing the pentagrid/Penrose idea: https://www.math.brown.edu/reschwar/M272/pentagrid.pdf 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), pp.1-7. 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: http://www.ams.org/publicoutreach/feature-column/fcarc-ribbons The Empire Problem in Penrose Tilings by Laura Effinger-Dean: http://www.cs.williams.edu/~bailey/06le.pdf Pentagrids and Penrose Tilings by Stacy Mowry & Shriya Shukla: https://web.williams.edu/Mathematics/sjmiller/public_html/hudson/HRUMC-Mowry&Shukla_Pentagrids%20and%20Penrose.pdf Penrose Tiling by Andrejs Treibergs: http://www.math.utah.edu/~treiberg/PenroseSlides.pdf Algebraic Theory of Penrose's Non-Periodic Tilings of the Plane by N. G. de Bruijn: https://www.math.brown.edu/reschwar/M272/pentagrid.pdf Particularly good and helpful, and (we think) an undergrad thesis which is impressive!: http://www.cs.williams.edu/~bailey/06le.pdf An interesting popular science read on the discovery on quasicrystals and their connection to Penrose Tilings: The Second Kind of Impossible by Paul Steinhardt: https://bookshop.org/books/the-second-kind-of-impossible-the-extraordinary-quest-for-a-new-form-of-matter-9781476729930/9781476729930 Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics Link to Patreon Supporters: http://www.minutephysics.com/supporters/ MinutePhysics is on twitter - @minutephysics And facebook - http://facebook.com/minutephysics Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute! Created by Henry Reich