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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/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
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Created by Henry Reich
I started this video thinking this was just a weird feel-good pseudoexplanation of aperiodic tilings, then you just blew my fucking mind
@DSYNC-RONIZED Says:
rin penrose
@itsmewonder5041 Says:
The background music is not good.
@LunarcomplexMain Says:
Could prolly just summarize that since there appears to be some center to this formation, that over laying a copy of itself anywhere else but the center wouldn't be possible
@quiethiYour999ping Says:
satan
@gnenian Says:
PEN
ROSE
TILS (The End of Infinity)
I'll get my cape 🧛
@therongjr Says:
I hate these so much.
@mossy8419 Says:
5:31 interestingly I happened to encounter this exact number working with a completely unrelated problem (cubic equations) because this number is one of the three roots of x^3 - x^2 - 2x + 1 = 0. Its exact value is 2cos(π/7), which is because that cubic equation happens to be a factor of the seventh degree polynomial which gives the seventh roots of unity. I can’t find any relationship between this number and measurements on a heptagon, but it is the length of one of the chords spanning two vertices on a regular unit 14-gon.
@erawanpencil Says:
@4:30 Can anyone clarify what he means when he says it's a "frequency vs period thing"? I thought period was a measure in seconds, i.e. in time. These tiles are fixed geometric objects. What's he referring to regarding period?
@Amy-m2i7r Says:
Fold symmetry 14, max disorder, pattern 0.24
@xemkis Says:
I will never be satisfied until i have a rug, curtains, or some other subtly patterned decoration in my house with a penrose tile pattern.
@you2tooyou2too Says:
Should have been called Pentrose grids. ;-)
@ZacharySuhajda Says:
Iv always wondered what they meant by "didnt repeat" for the longest time and I was ready to watch the whole video for an explanation on how they dont repeat at all and 20 seconds in I got the explanation I had needed on what they meant by "didnt repeat"
@ChadFaragher Says:
Maybe I'm autistic, but when I listen to the marimba music I hear your voice. Is the audio of your voice an input to the algorithm that generates the music?
@nokia-gm8gv Says:
that nice
@qwertyuiop.lkjhgfdsa Says:
4:03 looks kind of like a cat face
@ruperterskin2117 Says:
Cool. Thanks for sharing.
@ZILtoid1991 Says:
🅱️in 🅱️en🅱️ose 🅱️ilings
@gamingchanneIgaming Says:
what is this song bro
@noway8233 Says:
Cool graphics , they looks great 😅i like Penrose , he was very smart and funny 😊
@mikermiks5784 Says:
I can see repeats
@1harlo Says:
thank you for explaining that when I see a pattern and someone says “there’s no pattern to this mathematically” that there actually is and we’re not crazy
@Rolandais Says:
I feel like, it's a how it doesn't repeat, not a why? The why, is, because it was designed to never repeat, it's the how it never repeats, that is in the proof? Right?
@glajskor90 Says:
SIGNALIS
@Makememesandmore Says:
I know how you made the music
@Sockman509 Says:
You didn't have to make the music never repeat either 💀
@Ra-ue2ss Says:
music in the background is really annoying
@kilroy987 Says:
0:41 So they do repeat, just penta-radially, not on a perpendicular coordinate system.
@FourthRoot Says:
The interesting thing is that any subset of this tiling, no matter ho larger, actually occurs an infinite number of times, just not at regular spacing.
@Pasakoye Says:
Neat stuff.
@20xx-mm-dd Says:
the "music" is driving me crazy
@itamareizikovich Says:
I am convinced that math is the literal god.
@davecorry7723 Says:
Interesting.
@Braskil Says:
Hmm I was thinking the tiles in the bathroom looked a bit boring anyway...
@agusavior2 Says:
4:26 here is the proof
@Kronyx-k3r Says:
great video
grating song
@olivia_am3230 Says:
“Infinity ratio” 4:51
@fenderchen182 Says:
Wouldn’t some tilings end up being rotationally symmetric?
@normi3s_ge7_0ut Says:
Im warning you right that nobody knows what youre talking about but theyre all nodding and agreeing with you
@user49917 Says:
I have used your grid logic in a very interesting way. This has been eye-opening. Thanks for this insight.
@Ruhgtfo Says:
Seems like ECC RSA. Noise with prime's
@Gabrielrandom-l6y Says:
so... where are the RIN tilings?
@JamesR624 Says:
0:07"They never repeat themselves."
0:12 "There are patches that are perfect matches."
Yeah, see this is why mathematicians are not linguists. They sometimes struggle with the actual definitions of words.
Spoiler: They DO repeat themselves, a LOT. But if you just squint, and then throw out the definition of the word "repeat", then they "don't repeat themselves". 🙄
@chekote Says:
Video: intelligent lesson about math and geometry
Me: 1:23 oooh, a heart
@__________________________hi52 Says:
01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001...
Does this repeat?
@Spoon97 Says:
This video relieved my 2 week long constipation.
@hermask815 Says:
Any hardware stores selling parts for Penrose tiling?
@suhnih4076 Says:
Wow
@AndyZach Says:
Like you, this is the first time I've seen a good explanation of Penrose tiling. Thanks for the explanation.
@prbprb2 Says:
I would like to know what the Fourier transform of (the lattice sites) of a pentagrid. Does someone have a reference.
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