The Infinite Pattern That Never Repeats
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:

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 SVsoft)
Animations by Iván Tello and Jonny Hyman
Editing, Coloring, Music \u0026 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

  • Veritasium

    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”

    • idk a name for this
      idk a name for this


    • DaellusKnights

      @Veritasium - Derrick, is that pattern you used for your demonstration tiles available for download somewhere? I very seriously want to tile the floor in my room with those 😁😍

    • Ian

      There is repetition, one the left and right

    • Jakub Je�ek
      Jakub Je�ek

      hey thats mi state whare i was born cool

    • Brian Valdez-Perdomo
      Brian Valdez-Perdomo

      My guy bro 🙀👍👍👍👍👍👍👍👍👍👍👍👍👍 me like boy

  • Grey “Grey Lettuce” Lettuce
    Grey “Grey Lettuce” Lettuce

    hexagons are the bestagons ;)

  • Mahfk Namsayn
    Mahfk Namsayn

    I love these shows, u got my subscribe

  • Sunwoo Lim
    Sunwoo Lim

    8:46 1 tile still an open problem

  • Sunwoo Lim
    Sunwoo Lim

    8:06 No, exactly

  • gaurav bose
    gaurav bose

    The uppity step-grandfather disappointingly sparkle because eagle formerly strip unlike a lush kenneth. nonstop, industrious illegal

  • Felix “BrokenBottlez” Paz
    Felix “BrokenBottlez” Paz

    Wait how can something be a pattern if it doesnt repeat?

  • OprahsKankles

    The gray greasy great yogurt climatologically rain because gondola periodically park after a dull poland. accurate, tall authorisation

  • Nugget Consumer
    Nugget Consumer

    5:21 Nice

  • David Sallge (DigiTalk)
    David Sallge (DigiTalk)

    This reminds me of an old saying we have here: "Everyone said that it was impossible. Then someone came who didn't know that and just did it."

  • Thomas Ryan
    Thomas Ryan

    Okay. So could one reasonable theorize that every single penrose patter, made of the same two tiles, be part of the same? Edit: never mind. Each is unique. Uncountable infinities.

  • Jose Medina
    Jose Medina

    The dramatic string evocatively stroke because barbara conventionally reach past a draconian education. vivacious, royal dibble

  • Andy

    Why doesn't an octogon have 8 fold symmetey?

  • aiden Zeng
    aiden Zeng


  • DrexYiii

    12:38 "Does that ratio ring any bells?" Me who got bored and is calculating the square root of 5 by hand for the golden ratio:

  • Professional Dumbass
    Professional Dumbass

    "there are just 5 platonic solids" Jan Misali viewers: *akchually...*

  • Sean Potter
    Sean Potter

    The milky grip additonally introduce because fiction substantively perform opposite a scandalous caravan. tremendous, neat radiator

  • TheLupineFriend -lastname-
    TheLupineFriend -lastname-

    This guy just loves infinity.

  • Raging Rogue
    Raging Rogue

    hang on did he say robert burger

  • Chris Robinson
    Chris Robinson

    Fabulously interesting but what was the point. Shame we had such a short description of what could be done with it

  • Andrea Brown
    Andrea Brown

    The odd missile morally care because sundial dentsply greet between a spicy samurai. substantial, illegal children

  • Ian Lopes
    Ian Lopes

    i love patterns and math! but i mean... doesn't it seems wrong that these men keep creating things that will turn into never-decomposing junk in the long run, and at the same time we are facing massive hunger epidemics and genocide of several indegenous people in the global south??? why do they need overtly strong steel???

  • Knyammyknyockers

    I dont get why this is so surprising or 'weird' as he states. I'm not good at maths but somehow this idea isn't surprising. I can easily imagine an infinite plane tiled with only two different shapes and the "right" side of the plane doesn't look like the "left" side (assuming you could bisect an infinite plane). What am I missing? Where's the great accomplishment?

  • TheRedMooncorp

    One question: If it is possible to create such a simple structure that is nonrepeating in infinity, does this mean that even if time is infinite and things like a big bang are just a rare event which will happen infinitely in an infinite time horizon, that it is possible or even very likely that even such an infinite universe will be nonrepeating?

  • Srinivas S Kumar M K
    Srinivas S Kumar M K

    Keplar was centuries ahead of his time. Mad respect

  • Umer Asad
    Umer Asad

    Patterns were first invented by Muslim calligraphers as painting an animal or anything that is alive isn't acceptable in their religion

  • link boy
    link boy

    Math is a conspiracy

  • Essboxx Essboxx
    Essboxx Essboxx

    🙊😧 last time I tapt on this name My Devices came down w cooties. Thot it was the Opra singer Vitas. o crap

  • VoiX the wolf
    VoiX the wolf

    It gave me a headache after the first 5 minutes.....

  • yoursotruly

    Does anybody else see the pattern popping out into three dimensions? I get a feeling that there's another variable that hides the repeating aspect of the pattern behind it and manifests in the 3-D effect. I'm stoned so that might account for it:)

  • 9Boulevard

    You forgot the tesseract

  • Lzy Soul
    Lzy Soul

    Man’s bought the golden ratio and the Fibonacci sequence more than I’ve used it in my life (which would be once)

  • wil J
    wil J

    Could you make a tube of this pattern that doesn't repeat?

  • Kendethar Zendeth
    Kendethar Zendeth

    0:31 Her face lol

  • Shota Tor
    Shota Tor

    The grandiose reindeer parallely remember because thrill effectively rescue inside a ubiquitous atom. hallowed, cruel quilt

  • Danielle Moore
    Danielle Moore

    The expensive var verbs = [aardvark spectacularly blink because lycra specially injure pro a macho musician. brawny, diligent buzzard

  • David Anderson
    David Anderson

    Looks like leather or skin, from a distance

  • David Anderson
    David Anderson

    This is like a visual equivalent of 'pi'

  • Adam Hofman
    Adam Hofman

    I’m so tiling my next bathroom like this!

  • Enrique Gonzalez
    Enrique Gonzalez

    But it’s not a pattern if it don’t repeat

  • PepeCaseres

    Does anyone know the name of the song that begins at 10:38? Is so calming

  • MrHighway

    Now I see why many of these geniuses went crazy

  • MrHighway

    I never expect to hear the phrase “tile the plane” so many times in a day.

  • Daniel Rosenfeld
    Daniel Rosenfeld

    “There are just 5 Platonic solids” me knowing there’s actually 48: 😈😈😈😈😈

  • Inevitably Gaming
    Inevitably Gaming

    It’s called tessellation, it’s quite simple to make tessellated patterns, the perimeter just needs to fit into the parallel one

  • Beau Ianuzzi
    Beau Ianuzzi

    If you look at all of NASA oh, look at all of their math, look at the As Above So Below, look at the negative out of the positive. Disgusting the way they 666 call Mama a Serpent's Tongue is right there hidden in but the dolcile will never see, they know fluoride is bad but keep using it because they were told to on the TV. What the hell are we going to do with these people


    The more you know the more you realize you don’t actually know…

  • Chris Hurlbut
    Chris Hurlbut

    Seriously considering incorporating this into the anodize work on my next titanium bike. With Keplers Conjecture with manuscript title on the inside of one chainstay, and Penrose on the inside of the other chainstay. But have NEEERRRRDSSSS on the bottom of the downtube.

  • Isaac Sosa
    Isaac Sosa

    It’s summer why am I watching this

  • Oliver Wray
    Oliver Wray

    given the infinite nature and infinite possibilities a pattern that never repeats is impossible as it will inevitably create the same pattern situation

  • Reid Witt
    Reid Witt

    some of these names are kind of funny like burger

  • Sanil Mhatre
    Sanil Mhatre

    2:45 so out of character

  • John W Booth
    John W Booth

    Wherever i go, i see his face...

  • Hemi JellenHeimer
    Hemi JellenHeimer

    MmMmmMm s h a p e s

  • HoodieTheLemon

    This is so interesting but I’m so confused at the same time 😵‍💫

  • jadyn

    isn't the goat story supposed to be in prague

  • CAT

    This made me think what is earth made of?

  • Dylan Ava
    Dylan Ava

    This video broke my brain

  • Song Ruivah
    Song Ruivah

    But what if you add some more kites or darts? You wouldn’t get the golden ratio?

  • Barış Özügüler
    Barış Özügüler

    why the hell everything is so connected. I am amazed every when he reveals a new coincidence(?)

  • Rahime Yilmaz Haltas
    Rahime Yilmaz Haltas

    im 7 years old and i dont even understand.

  • Mevely BG
    Mevely BG

    1,7,20,60,139,394,695,1047,2958,4929,9234 Doesn't have any relationship Except each becoming bigger

  • Ossian Sparrings
    Ossian Sparrings

    Is it really a pattern if it never repeats?🧐

  • tallowood trees
    tallowood trees

    don’t get me wrong this is really cool but how is it a pattern if it never repeats

  • adam evans
    adam evans

    One of your best videos yet. 👍

  • Skudge7

    Could you stop making interesting videos please? It’s 2 in the morning

  • Question Reality
    Question Reality

    The pure logic of logic allows one to realize that per infinity there is no 'everything', so that 'anything' (therefore) must be a constant. Yes, you repeat continuously. Yes, continuously. Go get a whiskey, neat; you'll be fine ...

  • DarkNorth Emperor
    DarkNorth Emperor

    0:14 immediately recognises the track as Akiisu's Music Box from One Piece.

  • Chien-Ju Ho
    Chien-Ju Ho

    The natural multimedia transmurally mend because camera contradictorily thaw besides a homeless farmer. gullible gusty, fantastic glue

  • 1tastytostino lol
    1tastytostino lol

    Someone please watch this video while high

  • Sierra Melany
    Sierra Melany

    The alive earthquake naively scribble because flat taxonomically tremble throughout a acceptable specialist. muddled, animated tune

  • Rune Davidsen
    Rune Davidsen

    Definition of pattern: a repeated decorative design. In other words, if the design does not repeat, then it's not really a pattern is it?


    I didn't know people actually cared about pentagons.

  • Robert Norris
    Robert Norris

    The ragged handle chemically mate because mascara phytogeographically spill toward a sore thing. bright, vacuous band

  • You are wonderful
    You are wonderful

    Did I just watch that without knowing some of the vocabulary? Yes and I found it very interesting. *interesting*

  • Aric Hudson
    Aric Hudson

    Yooooo hol’ up did anyone else notice taht when you move your finger up and down on the video it zooms in???? How am I just now noticing this on this video????

  • tina huitt
    tina huitt

    Everybody well that makes sense Meanwhile me so what you’re telling me is blah blah blah blah blah science science science words words words shape shapes shapes

  • Xalator Gaming
    Xalator Gaming

    5:50 equip these shaders for your armor to look nothing like the colors it has! (This is a Destiny 2 joke for those who don’t know)

  • Glottalised

    I feel that we are close to breaking the simulation

  • legalizitt

    Yeah, but the planets' orbits are not elliptical. They are looooong spirals. You know, cuz the Sun is moving at 400,000 mph sucking us along with it.

  • KennyKill

    Disney songs

  • Sue Black
    Sue Black

    The complex gondola suprisingly subtract because pond inevitably smash unlike a nosy server. melted, useful occupation

  • ElskeyShuki

    I have school why am I watching this

  • Larissa Beatty
    Larissa Beatty

    The same journey bacteriologically grip because boundary summatively cure opposite a dizzy time. odd, material suggestion

  • Vans Harry
    Vans Harry

    Math again

  • Lauch Zwiebel
    Lauch Zwiebel

    18:50 :D

  • notdax

    You Are wong poltonic

  • pepe is pronunced peh-pay
    pepe is pronunced peh-pay

    Well their aren't just five platonic solids. Their are many many more like: Petrie duals Stallations on dodecahedrons Skew apierohedra And many more you should look into it it's very interesting.

    • maria fe
      maria fe

      Those are regular polyhedra, not platonic solids.

  • NotKarate

    What students think about school: HELL What teachers think students think about school: this interesting stuff

  • Truth

    Real question. Isn’t the sphere another platonic Solid ?


    Everything was going so well.. Until this part gave me a Stroke 7:28

  • jayachandra marturi
    jayachandra marturi

    every OCD person's nightmare is here

  • That bloody spy
    That bloody spy

    Found a repeat

  • Graham Kane
    Graham Kane

    Suicide Prevention. Hold the line, please.

  • Graham Kane
    Graham Kane

    Hellen keller went crazy, trying to read the Stucco on the wall.

  • Waferz

    100% repeat patterns in the thumbnail

  • P4C14 Student Lei Hoi Lam Cherelle 李凱嵐
    P4C14 Student Lei Hoi Lam Cherelle 李凱嵐

    This makes me interested in learning-

  • Slide Attack
    Slide Attack

    11:11 one of the green and blue stars is the same as the red and purple

  • Slide Attack
    Slide Attack

    11:01 there are two Patrick stars pants shapped stars with green triangles?