The Infinite Pattern That Never Repeats

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Simple rules of geometry meant that 5-fold symmetry was impossible as were crystals without a periodic structure. This turns out to be wrong. Thanks to LastPass for sponsoring a portion of this video. Click here to start using LastPass: ve42.co/LPs

Huge thanks to Prof. Paul Steinhardt for the interview on this topic. Check out his book ‘The Second Kind of Impossible’

If you'd like to learn more about Penrose tilings, go check out "Penrose Tiles to Trapdoor Ciphers" by Martin Gardener, which helped my research for this video.

Filmed by Gene Nagata (Potato Jet on JPvid)
Animations by Iván Tello and Jonny Hyman
Editing, Coloring, Music & Audio mastering by Jonny Hyman

Prague scenes filmed in 2012.
Special thanks to Raquel Nuno for helping with the tilings!

Additional Music from Epidemic Sound









コメント数 22 674
Veritasium 年 前
Roger Penrose was just awarded the Nobel Prize for Physics! Not for this pattern but “for the discovery that black hole formation is a robust prediction of the general theory of relativity”
Wayne Hieatt
Wayne Hieatt ヶ月 前
Hi, I've had a burning question since highschool physics (I failed btw). We were taught that gravity was one of the fundemental forces, and I beleive that is still taught. But Einstien tells us gravity is the curvature of space-time, so to my thinking, that makes gravity a resultant force, ie the bending of space-time is the result of the interaction of space-time and energy (in the form of matter). My question: is gravity the result of the curvature of space-time or is that curvature the result of gravity?
Repent!. ヶ月 前
Repent to Jesus Christ!! “My help comes from the Lord, the Maker of heaven and earth.” ‭‭Psalms‬ ‭121:2‬ ‭NIV‬‬
TigerElly ヶ月 前
Snow Chrysant
Snow Chrysant ヶ月 前
both Einstein and Penrose: Suffering from Success
Universal 2 ヶ月 前
Message Filterer
Message Filterer 8 時間 前
Justin Pierce
Justin Pierce 11 時間 前
Hexagons are the bestagons
Shaka Zulu
Shaka Zulu 17 時間 前
Okay, so you've said it several times but you never showed the proof that it never repeats. How would you even do that? The bigger question I guess is why you would ever do it? Show your work lol.
AlmostFrosty 日 前
i some how understood everything and misunderstood on how i understood
1 日 前
9:56 me trying to organize hole-punched paper
Mikrokosmos 2 日 前
this is actually so cool
Jan Knoblich
Jan Knoblich 2 日 前
1:20 what about a sphere?
Waffle gaming
Waffle gaming 21 時間 前
well, technically. it can be rotated by any degree and look the same, but I'm not sure if that invalidates it or not.
Thomas Walsh
Thomas Walsh 2 日 前
I’d like to see the proof that there is an uncountable infinity of penrose patterns
NO_One 3 日 前
so what your saying is that... its not a pattern?
S E 3 日 前
More than a year has passed since u uploaded this vid. Now the most important question... What have u done with this big packages of plastic crap?? I hope u load now a pic of ur bathroom into the net, just to show u gave this crap a 2nd life and used it to replace old ceramic tiles. It would be to bad, if u have had throw it away. SUSTAINABILITY is the magic word. Plz load up a pic to show me that u r not evil ;-(
Only for study
Only for study 3 日 前
Now I can even find golden ratio in 4 step Triangle. 🥴
Only for study
Only for study 3 日 前
Next Sunday is my math exam. I thought my geometry preparation was completed. After watching this video, “I have many thing to learn”.
Brandon Bakes!
Brandon Bakes! 3 日 前
Dang he said periodic and periodicly so many times.
theVasile 3 日 前
wtf is this comment section
Waffle gaming
Waffle gaming 21 時間 前
*Purple-Guy* 3 日 前
Vsauce would be friends with you.
RandomJolteon 4 日 前
1:21 have you stumbled upon the video known as “There are 42 Platonic solids.” ?
Cecilie Conrad
Cecilie Conrad 4 日 前
Not just because of this video, he's a genius in general.
Cecilie Conrad
Cecilie Conrad 4 日 前
Give this man more credit, he is a genius.
wilbur 4 日 前
That is the fabric of The Matrix
wilbur 4 日 前
Those are really cool video thank you for bringing that up. those patterns are amazing
Justin Cronkright
I know it's just post-knowledge in a sense. But it seems odd to say 'Quasi-crystals' were impossible. Best and seemingly from the start I considered them just not produceable en masse in our average/daily ways (it isn't practical for life & once you get life started on something very basic such as in geometry/trigonometry, then you largely just carry on forward building upon the basic rules of that route). This is especially true given the general constraints and directedness that most life on the planet has to maintain.
josh johnson
josh johnson 4 日 前
it has been a long time since i've had my mind blown this bad
curly fries
curly fries 5 日 前
6:08 Robert Burger. My favorite part of this video
Waffle gaming
Waffle gaming 21 時間 前
antari 5 日 前
CGP Grey: Hexagons are bestagons, they tile the plain perfectly! Mathematicians: But what shape(s) tile the plain in a perfectly imperfect way?
hung nguyen
hung nguyen 6 日 前
The paradox symmetrical layout seem like it would work well in class room that have 3 or more students each tables that looking at each other...this doesn't work at restaurant and cafes tho the table layouts
John Christophel
Wow. mind blown. It's like an everlastinggobstopper was for endless over lapping taste in Willy Wanka. I'm going to be mentality chewing on this for a while. I'm realizing new meta-materials, inspired now, getting busy. Super Thanks!
Ethan Finke
Ethan Finke 7 日 前
Today I learned Prague has more than just the king Kong balls
Just account
Just account 8 日 前
Actually a Czech Person :)
VersionDust 8 日 前
I- But I saw a repeat-
keerthi vasan
keerthi vasan 8 日 前
By the angel 36 and 72 at the intersecting of kite and dart, I could interpret something it's 108° if we can possibly add reuleaux triangle kind of curvature to that will it still remain aperiodic tiling it has multiple applications if we can crack into this
Shanee 8 日 前
how about 3 dimensional shapes
A sentient Brick
technically, there are 48 platonic solids
VikiKookie 8 日 前
Something can exist if it wants to. You wanna make a machine that sucks up bad air and freshens them? MAKE EM like i understand it’s hard but.. I can make up a word.. Endolindori Y’know what that means? Someone that doesn’t believe in the end of life Ehblessconmeheto It basically means die.
It isn't exactly a pattern if it never repeats
Zoom bec!
Zoom bec! 9 日 前
The thing about the world I know that this is nothing about the vid but u know the Big Bang they where 2 rocks then so how it made humans and the earth so we should respect rocks because they made us but this does not sound true that’s why the evolution belief is just a random fairy tail. Think about it before believing it.
Waffle gaming
Waffle gaming 21 時間 前
the big bang was not two rocks. rocks did not make us. and how does this disprove evolution?
GamingGuy 9 日 前
Nathan 9 日 前
Penrose tilings is just overlapping circles
TTVHateful 9 日 前
The definition of pattern is something that repeats infinitely and so a pattern that doesn’t repeat ISNT A PATTERN.
Theron Brown
Theron Brown 10 日 前
You should see the phycadelic patterns...check out the flower of life it's very interesting pattern
nolifer 10 日 前
you was in czech republic? lol i live there.
T4Seven 10 日 前
If it never repeats, doesn’t that make it…. NOT a pattern?🤨
Wan 10 日 前
lmao my head almost combusted
Rontech140 11 日 前
best party floor design
Meows Lessons
Meows Lessons 11 日 前
im moar confuze help meeee iv lost me spelin
Trent Shuey
Trent Shuey 11 日 前
I love thinking about how this concept applies to rhythmic subdivision. Are you a musician?
Perish. 11 日 前
An extraterrestrial Quasicrystal has been found and is said to be 4.5 billion years old (Princeton University with help from NASA found this.)
Nizati 11 日 前
Listening to this makes me feel like this right here where magic and math overlap somehow. Like.. five and infinite are hand in hand in a weird ass mathamatical way, but somehow we knew that all along . I know I know, evil how dare I bring in such nonesense but...... To an outsider that only know the very basics, this stuff seems like magic, you know?
Spear_Dud 11 日 前
The apple of our pi
To me its insane how an almost random theory, sprouting from Keplers incorrect assumption about the nature of the universe, led to the creation of new electronic pieces and materials. No matter how you slice it, math has practical use in everyday life. All these numbers and equations that we learn in school arent just number, they're just a small fragment of a much larger picture of tactile, everyday objects and phenomenon. I know its hard to explain and I'm getting a little philosophical. But its crazy how a never-repeating pattern can have such practical uses, and tie into so many other mathematical phenomenon such as the golden ratio, snowflakes, and crystals.
James Castelli
James Castelli 12 日 前
What I don't understand is if one can zoom into small sections of just several tiles that are identical, but exist in different "infinite" sets, what obliges each to extend differently than the others??
Nathan Ricard
Nathan Ricard 12 日 前
Here is a interesting question. Could you or some other smart person, create some set of 3D shapes that stack together aperiodically? A 3D analog of the Penrose tiles. A bunch of cubes can stack periodically as we know, you showed how spheres can stack in the canon ball example. But what about tiling a 3D volume with other shapes?
Clover Lucky
Clover Lucky 7 日 前
Technically, spheres can't stack periodically due to the gaps between the shapes, however, it is still a repeating pattern. I believe triangular pyramids should be able to stack periodically and be a repeating pattern. As for a set of 3D shapes that stack together aperiodically, I don't think it'd be impossible, perhaps using cubes as a base might work. However, I have no idea. I am not a mathematician, just someone who stumbled onto this video through the mysterious ways of the algorithm.
Hasan jaha
Hasan jaha 12 日 前
Kids, don't watch this while high...
cruithne_2292 12 日 前
You lost me at the word "Tile" where I started to think about the tiles in my kitchen and whether I should order a pizza for dinner.
Owowy 12 日 前
This video was posted on my birthday and it’s an insane vid, nice pattern ^^
Kim Jong-un
Kim Jong-un 12 日 前
Still no clue what i just watched lol
Weill 13 日 前
That’s tripy
Andi Front
Andi Front 13 日 前
I still don't get why the 440 kites and 272 darts lead to the golden ratio. I mean what if I just add one more than it's not phi. I'm not to sure because maybe it's meant to refer to a complete pattern where all edges are round but still little confusing.
DarkSlayer_2525 13 日 前
I only see the dices of dnd
maria damien
maria damien 13 日 前
Firoer Blaze
Firoer Blaze 13 日 前
OMG i live next to czshech
Dyktafon 216
Dyktafon 216 13 日 前
Cube? Icosahedron? I think you meant d6 and d20.
MaynardOwns 13 日 前
That look like geometric I’m tripping balls shapes that someone smart enough managed to use for science
Edwin M
Edwin M 13 日 前
I wonder if our entire universe is patterned this way. It would make sense as to why we wouldn't be able to find similar star systems near us. Infinity is a big number.
austin Emily
austin Emily 13 日 前
Did anyone else just stare at the thumbnail and search for 2 of the same??
SFLaMadness 954
SFLaMadness 954 13 日 前
Idk I see some that are the same
Zachary 14 日 前
Patterns repeat by definition.
Keyboard Smash
Keyboard Smash 14 日 前
I thought it was my life
Spamton G. Spamton
1:22 now do a rhombicosidodecahedron
Jamie Donner
Jamie Donner 14 日 前
The house of bees .
Tony Kwan Ping Yee
Once talking science beyond school exam curriculum, it becomes interesting.
Hoseok 250 Boxers
I am watching this at 3 am. No info entered my brain.
Jazzy Lee
Jazzy Lee 15 日 前
bro it just keeps going.... but it's so cool
denelson83 15 日 前
11:27 - Well, there practically may as well be only one such pattern.
Taco048 15 日 前
Ok math may not be that fun but shapes definitely are and I got no idea why.
Kazuto Kirigaya
Kazuto Kirigaya 16 日 前
JanLe 16 日 前
it‘s a little bit like quantum mechanics edit: this is so much maths interacting with each other, it‘s insane. I feel like anything has a sense now
Leandro Viana
Leandro Viana 16 日 前
There should be a movie about all these stuff, and Dan Shechtman would be portraited by Marc Maron.
Polyluchs Shroud
Polyluchs Shroud 16 日 前
I could watch these videos for day nonstop :)
Mohammad Ali Raza
One of the best videos I've seen on this channel.
sc2 sc2
sc2 sc2 16 日 前
technically speaking no pattern ever repeats if you view it as a whole
TheDestroyer5670 16 日 前
Can someone help me understand this. Every example of non-periodic patterns actually look periodic by Google's definition of "Having or marked by repeated cycles." Like the patterns clearly repeat it just takes a second to find the beginning and end of each pattern segment to see how it repeats. So what's the definition of a non-periodic pattern?
MyEaglesEyes 16 日 前
This seems very dumb. there has to be some weird kind of rule that they aren't explaining to even make this interesting because i can look at any of these patterns on the screen and find repeats that are even oriented the same way...
Le Xuss Lemon
Le Xuss Lemon 17 日 前
If it's infinite it has to repeat right? If not then the multiverse theory can actually be wrong?
Rafie Walker
Rafie Walker 16 日 前
Infinite things do NOT have to repeat.
Sébastien Gaudette
I failed science in high school
Mineplexian Gaming
i would like to be robin BURGER
Kid 👹
Kid 👹 17 日 前
9:43 is the best laugh ever
PheonixDeanix 17 日 前
If it doesn’t repeat then make only one
Phil MaCracken
Phil MaCracken 17 日 前
11:50 futile? Really?
Maxwell Barbe
Maxwell Barbe 17 日 前
As an avid dnd player, as soon as you pulled out the shapes I was like "Oh, a d4. Oh, a d8. Oh, a d12. Oh, a d20."
IBlood 18 日 前
I swear to god one minute i was watching youtube and now i'm trying to learn aperiodic tiling
Jake Smith
Jake Smith 18 日 前
Wait...are these people trying to say that this is how the Universe is constructed???
Rojan das
Rojan das 18 日 前
me stares at the video without understanding wt he is telling
def notHana
def notHana 18 日 前
As a child did anyone else press your palms to your eyes and start seeing this 12:08?
Affan Ahmed Usmani
Your explanation is amazing your are really amazing genius you must be amazing student you are a professor seriously because I saw your almost all videos for physics and math thank you for explaining this much good work
Ariel Gon
Ariel Gon 19 日 前
i decided to learn from this video instead of putting attention to french class
Roronoa Zoro
Roronoa Zoro 19 日 前
8:58 dont look when u high
Aboudi 19 日 前
A pattern that never repeats? Did they update the definition of pattern?
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