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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/res....chwar/M272/pentagrid

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/publicoutre....ach/feature-column/f
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/~trei....berg/PenroseSlides.p
Algebraic Theory of Penrose's Non-Periodic Tilings of the Plane by N. G. de Bruijn: https://www.math.brown.edu/res....chwar/M272/pentagrid
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-impo

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Created by Henry Reich