The Infinite Pattern That Never Repeats

30-Sen, 2020
7 368 381 Ko‘rishlar soni

Simples 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 UZworld)
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

  • 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”

    VeritasiumVeritasium14 kun oldin
    • ...which has nothing at all to do with this video.

      touristguy87touristguy873 kun oldin
    • Wait ... we didn't already know that? :O

      Flick PenroseFlick Penrose3 kun oldin
    • @Veritasium Is the Oxford's Mathematical Institute entry / courtyard ground pattern a Penrose one ? It looks like it. I remember watching an episode of an English series which story took place there and I spent HOURS in awe pausing and playing frame by frame each shot of the courtyard's ground pattern. Completely obsessed by it! Like a baby discovering that a rattle produces (annoying) sound... You can partially see it on Google Maps when you zoom in to the max here : But a Google image search will show better hi-res images. Thank you so much for that video, I didn't understood everything in it yet but at least I can stop obsessively dreaming of that ground pattern of Oxford Mathematical Institute! You've kinda stopped a kind of debilitating earworm song from driving me nuts by giving me, a curious asperger layman, the most comprehensive and accessible approach to patterns I've seen yet. My sanity and me are so grateful! Thank you! 🤯🥳🙏 (And also thanks a lot for the intense braingasm when you play with the 2 layers of film and the moiré aligns, it almost made me drop a tear) Cheers from curfewed Paris, the city of (turned off) lights.

      KyrilPGKyrilPG4 kun oldin
    • His research was based on the foundations of 2 unsung Indian scientists: AK Raychaudhuri & CV Vishveshwara. It was the Rayachoudhuri equation which inspired him. Proud to be Indian 🇮🇳🇮🇳

      Pranav PothanisPranav Pothanis4 kun oldin
    • Is it the same Penrose after whom the 'Penrose process' is named? A way to extract energy from spinning black holes by moving close to the exosphere?

      Pranav PothanisPranav Pothanis4 kun oldin
  • These periodic/non-periodic tilings are observed in the Islamic geometric patterns that are complicated but beautiful. Islam doesn't allow picturization of living beings like humans. This rule helped Muslims to grow the art of such wonderful geometric patterns. Note: These Islamic art of geometric patterns originated in the mooric Andalusia ie today's Spain. If I'm not wrong.

    The EntourageThe Entourage6 soat oldin
  • Mind blown! I need a lie down.

    Patrick HoeslyPatrick Hoesly6 soat oldin
  • He is the new vsauce

    Aviation HobbiesAviation Hobbies7 soat oldin
  • Ok, it took me a long time to realize how something based on so few tiles could go on forever "that never repeats", simply because that last part is not true. The patterns repeat all over the place, but never in a way that allow you to tile the plane using just any particular section. Because of the 5-fold symmetry, there's no way that they can form anything (under the vertex pairing rules that prevent the trivial rhombus tiling) that's a shape that will tile the plane by itself, since that would require symmetries of a triangle, square, or hexagon. But saying that it "never repeats" is just horribly misleading, because there are only a finite number of different possible vertex patterns, which obviously must repeat all over the place. You can have arbitrarily large sections of it that repeat somewhere else, but you can't construct the entire pattern from just those repeating sections.

    Steven GlowackiSteven Glowacki8 soat oldin
  • Ok, what hav i got to do right now in my life to understand thsi vid?

    armondtanzarmondtanz8 soat oldin
  • The hardest part is actually proving the conjecture lol.

    Somewhat Blank PaperSomewhat Blank Paper10 soat oldin
  • This is actually astounding. The concept and how it all ties up eventually in a way that approaches the golden ratio is actually so perfect.

    Jacob GouldJacob Gould11 soat oldin
  • I need that big d20

    Nutthatch WoodNutthatch Wood13 soat oldin
    • This is at least a hint at why re-evolution is eternal sync-duration connectivity.

      soinhu foitusoinhu foitu10 soat oldin
  • I was playing minecraft while watching this and got a villager with the infinity trade right when you said infinity here 18:30.

    AwesAwes13 soat oldin
    • Good job.. keep up the good work.?

      soinhu foitusoinhu foitu10 soat oldin
  • my brain melted and I want to tile the whole house

    çağatay tuncerçağatay tuncer13 soat oldin
  • uh huh

    Dan ZDan Z14 soat oldin
  • Bro people might never see this but there was a board game of this exact shape called Cirkus, with a purple box and board and it was this exact thing... I own it

    Fiesta_Blend458Fiesta_Blend45814 soat oldin
  • Well this video was definitely time consuming to produce. Thank you for making and sharing this with us!

    Mike O'BarrMike O'Barr15 soat oldin
  • Dam, Maths is so freakin cool!

    Luxray LloydLuxray Lloyd15 soat oldin
  • I'm pretty sure i did something like that when I was a kid (it wasn't infinite, but I did try)

    Luxray LloydLuxray Lloyd15 soat oldin
  • Why are people so confused? It's an interesting and clear message lmao

    Breno FariaBreno Faria16 soat oldin
  • Congrats to Penrose on winning the Nobel Prize! Fascinating video as always. It is amazing how these patterns exist in different fields.

    Professor PerryProfessor Perry16 soat oldin
  • Who else here's a child in the background? 10:31

    Ayden SibbernAyden Sibbern16 soat oldin
  • 1Password is leaps superior over LastPass.

    tabakstabaks17 soat oldin
  • This is the most intelligent illuminati confirmed video ive ever watched

    DRakeTR of KBamDRakeTR of KBam18 soat oldin
  • This is the most coincidence-filled thing I have ever seen in my life...

    2Tri2Tri18 soat oldin
    • then you probably don't know what the word coincidence means...

      Релёкс84Релёкс8418 soat oldin
  • Rrally interesting, but my guy are you really not saying that they are also dnd dice

    Ofir DolevOfir Dolev18 soat oldin
  • Wow

    Aleksander SowińskiAleksander Sowiński18 soat oldin
  • This is at least a hint at why re-evolution is eternal sync-duration connectivity.

    David WilkieDavid Wilkie19 soat oldin
  • Does anybody know where i can find the patter to print the tiling and transparency used to see the morie pattern?

    Lucas VidalLucas Vidal20 soat oldin
  • Drinking game : drink when he say 'periodically' or 'tile'. I'm bloated.

    Neil'sNeil's20 soat oldin
  • Rubic's club plays in here somewhere, right?

    Dean HowellDean Howell20 soat oldin
  • nah ill stick with Dashlane instead of LastPass

    VellwebVellweb20 soat oldin
  • The real mystery is how you spread these out all over your floor with multiple littles in your sphere and still maintained all the pieces. (Worm holes? Superposition? Nap time? Enquiring minds want to know.)

    Laure_leiLaure_lei20 soat oldin
  • Wow! Show me how to do that trick where you toss a polygon up in the air, and it morphs into a different polygon! That was really cool!! :-)

    Ken RossmanKen Rossman20 soat oldin
    • @Релёкс84 that was sarcasm on my part... :-)

      Ken RossmanKen Rossman18 soat oldin
    • it's called video editing

      Релёкс84Релёкс8418 soat oldin
  • Amazing - love it!!!!

    B88B8821 soat oldin
  • 18:04 Please, i would like to know more about such rules. Where can i find more info on that? Thanks.

    Solo Recibo SpamSolo Recibo Spam21 soat oldin
  • Maybe physics is not my cup of tea😑😞

    123 M123 M21 soat oldin
  • Duh ...

    john simsjohn sims23 soat oldin
  • Why does it need to follow the lines?

    Hamish ForrestHamish Forrest23 soat oldin
  • If math was this cool i would have paid more attention

    StibbleStibbleKun oldin
  • This guys travels, has an wxpensive hiuse full of toys. His life would be awsome if he didn't have that long term gf or wife or w/e.

    kaczan3kaczan3Kun oldin
  • This is the secret of the Zeppeli's infinitely spinning steel balls. ps: definitely not a JoJo reference

    Kono DIO daKono DIO daKun oldin
    • cringe weeb

      Релёкс84Релёкс8417 soat oldin
  • The question that occurred to me: is there a relationship between space-time and Penrose tiling?

    bofooit gojobofooit gojoKun oldin
  • do you have any friends to help you out there???

    Cabillo, John BenedictCabillo, John BenedictKun oldin
  • It turns out that he was Wang.

    Janezjanez NovaknovakJanezjanez NovaknovakKun oldin
    • What are your thoughts on the possibilities of encoding information within a quasicrystal structure? With the infinite possibilities of arrangement, it seems this should be

      bofooit gojobofooit gojoKun oldin
  • Washington DC

    Javier BordaJavier BordaKun oldin
  • te stai male

    Tommaso GambassiTommaso GambassiKun oldin
  • Bruh you did this for nothing, Military camo is also considered a pattern and yet never repeats since a repeating pattern in it would cause people to see it quicker.

    Memed TracksMemed TracksKun oldin
  • absolutely crazy that the tiles of the 2 tiles non-periodic shape matched up with what Kepler's drawing of a non-periodic shape. It's actually really profound to me that it matched up, it really puts us and our minds into perspective for me.

    Antonio GarciaAntonio GarciaKun oldin
  • Hi, there! I am amazed by your wonderful video! I am a professional translator and I would like to translate this particular video into Russian. It all sent shivers down my spine how 1 question leads to another... and another... and another... infinite :) Please contact me:

    Tony VeretyukTony VeretyukKun oldin
  • And yet even more evidence that there is an intelligent creator behind our beautiful universe. Don't hate me for saying it just look into the evidence! If you want Scientific answers, any of Josh McDowell's five books called The New Answers are great for that. If you want logic based research, my suggestion is The Case for Christ by Lee Strobel.

    Josh BowmanJosh BowmanKun oldin
  • At 2:13 please stop using the scp illustrated music it’s throwing my brain off

    Dawsieboy GamingDawsieboy GamingKun oldin
  • At 4:44 when rotating Keplars 5-way symmetry tiling, the centre point should be the star below your axis point instead of the decagon.. But yeah, how does one continue the tiling.. ;) Great video otherwise!

    Lach VogelLach VogelKun oldin
  • I don't know how many times this video blew my mind.

    Zane GantZane GantKun oldin
  • That's even tougher than watching Tenet..

    Cédric SCédric SKun oldin
  • wow! thanks

    fluke9fluke9Kun oldin
  • 1.58 I swear that is the music for a game and what is it called

    Sub because Why notSub because Why notKun oldin
  • Imagine this intelligent and without all the technology of today....f@!k me the astronomy stuff blows my mind

    Dean AshworthDean AshworthKun oldin
  • 22 over 7

    douglas mccanndouglas mccannKun oldin
  • half-life 3 confirmed

    Haytham Abdel-QaderHaytham Abdel-QaderKun oldin
  • What are your thoughts on the possibilities of encoding information within a quasicrystal structure? With the infinite possibilities of arrangement, it seems this should be possible assuming you can control exactly how the quasicrystal grows. If this is possible.. it makes the extraterrestrial origin of the only quasicrystal ever found very interesting. Could it be a message from a far off alien species? I think so. Shameless plug: More information in this video:

    Rather B. SquiddingRather B. SquiddingKun oldin
  • Is this like turning an irracional number into something physical?

    Liam Revorêdo PintoLiam Revorêdo PintoKun oldin
  • I just wanted to know a good tile pattern for the floor. I wasn't expecting a scientific lesson.

    TheManWithManyNamesTheManWithManyNamesKun oldin
  • The pictures of the two crystals that had electrons scattered off of them almost looks like the cross-section of a myofibril

    Trainer JBTrainer JBKun oldin

    Meagan BradyMeagan BradyKun oldin
  • Anyone else noticing the confused lady at 0:31?

    Sam Al-SaptiSam Al-SaptiKun oldin
  • this is just us looking at dimensions we cant see.

    • use this for mapping space

  • I was lost in the begining, but man, that was exciting to watch.

    EvandurilEvandurilKun oldin
  • anyone here from science class👀

    boya hawkenboya hawkenKun oldin
  • Thank you for this great mental distraction. Putting my cat down today has had me feeling pretty terrible, but I was able to escape that for a moment while watching this.

    Graham McMullenGraham McMullenKun oldin
  • Make these patterns in glass, shine light through them, you need quite a few layers, you will find that the geometry of the light will change... It will gain mass.. exotic mass.. Use electromagnetic fields to control the mass that happens to flow through in just the right way.

    no one expected the spanish inquisitionno one expected the spanish inquisitionKun oldin
  • *me not understanding anything and coming into comments* . . . me after seeing comments: ah, I'm not the only one.

    bhishma pitamahbhishma pitamahKun oldin
  • Got It So We Have A d6,d4,d8,d12 and a d20

    Mathew SilvaMathew SilvaKun oldin
  • Great research work!

    Jérôme TOUATIJérôme TOUATIKun oldin
  • And this is the solution to the COD Mobile Puzzle

    Binge SquadBinge Squad2 kun oldin
  • How do you do this good of educational stuff?

    Mr.Spoon025Mr.Spoon0252 kun oldin
    • useless skill

      minij hooiminij hooiKun oldin
  • What if this is how the atoms of the 2nd dimension work.

    Anuj BhandareAnuj Bhandare2 kun oldin
    • That was brilliant.. thank you!!!?

      minij hooiminij hooiKun oldin
  • OK this time he has succeeded to hurt my eyes and brain at the same time

    N m NN m N2 kun oldin
  • 11:50 kore ga requiem da! after 5 seconds

    Killer QueenKiller Queen2 kun oldin
  • Beautiful!!!

    rrawwbbrrawwbb2 kun oldin
  • Man penrose is 89 and still kickin!

    Magnum Dong AdventuresMagnum Dong Adventures2 kun oldin
  • The problem with a pattern that never repeats is that a pattern is, by definition, supposed to repeat.

    TheironswordTheironsword2 kun oldin
    • 1101001000100001000001... this is a pattern that never repeats. A pattern absolutely does not have to repeat.

      Релёкс84Релёкс8418 soat oldin
    • I have sewing patterns with no repeats, and when I open my phone's lock screen, I trace a pattern to do so. Only repeating patterns repeat.

      Laure_leiLaure_lei20 soat oldin
  • Question - What is the significance of the colour variations in the tilings shown (around 04:00)? The rhombus pattern as shown has three colours, then equi triangle and square has only 2, then hex has 4?? Is this just arbitrary in the video presentation, or is there a reason or significance for these differences? The first hex pattern showed one colour only. In the last "six-fold, spinning" presentation, there are four different coloured hexagons, and if you rotate 60* (for example), sides align but colours do not.

    Nathan TaylorNathan Taylor2 kun oldin
  • i love this because... how could you not, but i hate it because now i feel like a total idiot

    jman tjman t2 kun oldin
  • I'm sorry to say this, but your title is redundant.

    TheBlueGuyTheBlueGuy2 kun oldin
    • did you watch the video?

      redbeam_redbeam_Kun oldin
  • "there are no quasicrystals, just quasi-scientists" sounds like someone who's jealous they didn't figure it out first and or don't like actual science.

    Rem LezarRem Lezar2 kun oldin
    • Thanks rem lezar I always believed in you

      rzekarzeka13 soat oldin
  • yknow, the easiest infinite pattern that never repeats is just counting by 1

    yes noyes no2 kun oldin
  • 9:00 how can I get these sheets?

    Tom Norton-PlatfordTom Norton-Platford2 kun oldin
  • So your _definition_ of "repeating" explicitly excludes *rotation.* I'll say that's oddly specific...

    None of your BusinessNone of your Business2 kun oldin
  • Now i want to make a floor of those shapes.

    -Nameless--Nameless-2 kun oldin
  • Prague is that where the giant books were found? How does the fractals fit in to this story? Oh I should have just waited for the answer.

    Kristie HansenKristie Hansen2 kun oldin
  • useless skill

    FawnaFawna2 kun oldin
  • Great video - thanks! Aperiodic tiles existed already in the 1400's in Iran, according to Peter Lu. See this:

    David WahlstedtDavid Wahlstedt2 kun oldin
  • im brain fucked

    MultexMultex2 kun oldin
  • This was fun thank you!

    Nikolai WestallNikolai Westall2 kun oldin
  • mind blowen 🤯

    orfo70orfo702 kun oldin
  • this makes me miss vsauce.. it sounds like something he'd make a video on

    Flaming KarmaFlaming Karma2 kun oldin
  • Awesome video! One small remark: you are really only talking about rotational symmetry. For example, I would say "a square lattice has four-fold rotational symmetry". Namely, a square lattice also has reflection symmetries next to its translation and rotational symmetry. Keeping these in mind is important if one talks about general wallpaper groups.

    Luuk StehouwerLuuk Stehouwer2 kun oldin
  • Does anyone else want to make a floor tiling with these???

    Josh ColleyJosh Colley2 kun oldin
  • Thank You for delivering such a great piece of knowledge....your videos are interesting always

    samnan kadrisamnan kadri2 kun oldin
  • this is the way to generate random numbers that is good for encryption which is used in network and communications

    karma tseringkarma tsering2 kun oldin
  • The question that occurred to me: is there a relationship between space-time and Penrose tiling?

    CassieCassie2 kun oldin
  • Nosebleed pero ansaya hahahahha

    Bryan ValenciaBryan Valencia2 kun oldin