References
Here are a few links for further reading on Penrose Tiling:
- Brief Summary on Penrose Tiling (just use Wikipedia as an initial reading!)
- Aperiodic Tiling (with a little introduction on Penrose Tiling)
- Translational Symmetry
- Reflection Symmetry
- Five-fold Rotational Symmetry
- Prototile Definition (brief summary on prototile; once again, only use Wikipedia as an initial reading!)
Further reading for Quasicrystals:
- The Wikipedia page for quasicrystals is very technical and contains many esoteric explanations, so proceed with caution when reading it.
- https://www.vice.com/en/article/4x3me3/quasicrystals-are-natures-impossible-matter --> Here is an interesting article about how quasicrystals break our understanding of physics and their possible future.
Sources
"Forbidden Geometry" - Penrose Tiling in HYBYCOZO. (2016, April 16). Retrieved December, 2020, from https://medium.com/@TheConstructionZone/forbidden-geometry-penrose-tiling-in-hybycozo-8a9c6f427780
Gardner, M. (1997). Chapter 1: Penrose Tiling. In Penrose Tiles to Trapdoor Ciphers: And The Return of Dr. Matrix (pp. 1-12). Mathematical Association of America.
Geometry from outer space - Quasicrystal patterning in HYBYCOZO. (2016, April 16). Retrieved December, 2020, from https://medium.com/@TheConstructionZone/geometry-from-outer-space-quasicrystal-patterning-in-hybycozo-5485e79b8982
“Golden Ratio.” Wikipedia. Wikimedia Foundation, December 2, 2020. https://en.wikipedia.org/wiki/Golden_ratio.
Hayes, B. (2017, December 24). Sir Roger Penrose's Toilet Paper. Retrieved December, 2020, from http://bit-player.org/2017/sir-roger-penroses-toilet-paper
How to make a Penrose tiling. (n.d.). Retrieved November, 2020, from http://static1.squarespace.com/static/5754f47fcf80a16bffa02c45/t/57c6b9c5b3db2bd469e914e2/1472641508501/Penrose-instructions.pdf
Meisner, Gary, NF Hannibal, Patrick, Petes Farm, Simona, Sammy, Ebonygrace, et al. “The Golden Section / Golden Ratio.” The Golden Ratio: Phi, 1.618, June 12, 2014. https://www.goldennumber.net/golden-section/.
Meisner, Gary, Sasya Natasanthi, Liz, Amy, Kesang, Mohamed El Naschie, Bill, and Jason. “Penrose Tiling and Phi.” The Golden Ratio: Phi, 1.618, October 23, 2016. https://www.goldennumber.net/penrose-tiling/.
Meisner, Gary, Tara, Craig P.k Johnson, Sandor Szabados, Arthur, and Abhinav Smart. “Quasi-Crystals and the Golden Ratio.” The Golden Ratio: Phi, 1.618, December 21, 2016. https://www.goldennumber.net/quasi-crystals/.
Mutalik, Pradeep, and substantive Quanta Magazine moderates. “How to Solve Our Three John Conway-Inspired Puzzles.” Quanta Magazine. Accessed December 4, 2020. https://www.quantamagazine.org/how-to-solve-our-three-john-conway-inspired-puzzles-20201120/.
“Penrose Tiling.” Wikipedia. Wikimedia Foundation, December 2, 2020. https://en.wikipedia.org/wiki/Penrose_tiling.
“Quasicrystals Page.” Eric's Quasicrystals Page. Accessed December 4, 2020. http://www.physics.emory.edu/faculty/weeks/pics/icon.html.
Quasicrystals. Accessed December 4, 2020. http://www.geom.uiuc.edu/docs/forum/quasicrystals/.
Schultz, K. (n.d.). Penrose Tilings. Retrieved December, 2020, from http://jwilson.coe.uga.edu/emat6680fa05/schultz/penrose/penrose_main.html
Schweber, I. (n.d.). Penrose tilings of the plane. Retrieved December, 2020, from http://www.math.ubc.ca/~cass/courses/m308-02b/projects/schweber/penrose.html
Tomrocksmaths. “Tessellation, Penrose Tilings and Infinity.” TOM ROCKS MATHS, June 25, 2020. https://tomrocksmaths.com/2020/05/14/tessellation-penrose-tilings-and-infinity/.
Weisstein, E. W. (n.d.). Penrose Tiles. Retrieved December, 2020, from https://mathworld.wolfram.com/PenroseTiles.html
http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.html (Golden Ratio)
