The Infinite Pattern That Never Repeats

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 NOlocal)
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


  • Veritasium
    Veritasium16 dager siden

    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”

  • touristguy87


    5 dager siden

    ...which has nothing at all to do with this video.

  • Flick Penrose

    Flick Penrose

    5 dager siden

    Wait ... we didn't already know that? :O

  • KyrilPG


    5 dager siden

    @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.

  • Pranav Pothanis

    Pranav Pothanis

    5 dager siden

    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 Pothanis

    Pranav Pothanis

    5 dager siden

    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?

  • anTyfolium
    anTyfoliumTime siden

    *Your mind when you don't understand anything* : this video.

  • Filipe Lima
    Filipe Lima2 timer siden

    Math is AMAZING!

  • Pablo
    Pablo2 timer siden

    just stunning

  • True Indian
    True Indian4 timer siden

    little did he know that Roger Penrose would be awarded nobel prize few weeks of this video release. P.S- he has been awarded for his work in physics, not geometry. But he has been a multi-disciplinary giant!!

  • Geomegic DIY Coloring Pages
    Geomegic DIY Coloring Pages5 timer siden

    This was very interesting and inspiring! "Infinite Diversity in Infinite Combinations"! Spok was definitely onto something! 🖖

  • yasio bolo
    yasio bolo5 timer siden

    12ish: "it's futile!" No, it's a few tiles!

  • Wafikiri
    Wafikiri5 timer siden

    I have found an infinite number of infinite periodic 2D-tilings of equal regular pentagons and half as many same-side-as--pentagons' equal rhombs. The whole set is equivalent to the set of natural numbers, for a biunivocal correspondence can be made between both sets. However, I am not a mathematician and do not know whether anyone else has found these tilings before. Updated: Around 30 years ago, some publication assured that such rhombs and pentagons only could tile a limited surface, then periodicity was lost. Two hours later I had found two of the infinite periodic tilings I mentioned above. Only a few months ago I discovered the infinite number of such tilings. Updated: Once, I found out that some mineral had been found recently whose structure included limited pentagon-and-rhombs tilings.

  • yasio bolo

    yasio bolo

    5 timer siden

    these connections exist. Great video as always.

  • Telavus
    Telavus7 timer siden

    9:19 Can someone please link where I can buy these magic papers

  • Madalyn Rogers
    Madalyn Rogers7 timer siden

    im 11 in november and my mind has been blown 👁👄👁

  • Rick Lennox
    Rick Lennox8 timer siden


  • The Meme Man
    The Meme Man8 timer siden

    The infinite comment that never repeats.

  • Jalen MichalsLevy
    Jalen MichalsLevy8 timer siden

    18:56 For being so smart, Linus Pauling sure was an idiot on A LOT of things (see triple helix DNA, the non-panacea that is vitamin C, the example from this video)

  • Çağrı Bıkmaz
    Çağrı Bıkmaz8 timer siden

    Nice content

  • The Duck
    The Duck8 timer siden

    is that really a pattern if it never repeats

  • Silvio Francisco
    Silvio Francisco9 timer siden

    Wow!! Unbelievable! I have no words!

  • Georgescjh
    Georgescjh9 timer siden

    Greetings from Prague !

  • Nidhogg vom Walde
    Nidhogg vom Walde10 timer siden

    When I design the next bathroom....

  • Devin O'Driscoll
    Devin O'Driscoll10 timer siden

    Ultra Jurable Steel @ 19:17

  • Mason Hunter
    Mason Hunter12 timer siden

    Robert’s nonperiodic tiling looks periodic

  • OXMOND Tutorials
    OXMOND Tutorials12 timer siden

    Beautiful! 🤓👍🧡

  • John Smith
    John Smith13 timer siden

    Wow, one of the most compelling videos I have seen in years, not that I can admit to understanding much of it, but it makes me want to learn more. Purported relationships between the Golden Ratio and Fibonacci numbers? Fascinating!!! Its just like when someone says they understand Quantum Mechanics, and the response is that they haven't read enough about it ....

  • Daniel Amaral
    Daniel Amaral13 timer siden

    This is why I love mathematics. Everything is so perfectly connected, ie the golden ratio, the fibonacci sequence, penrose tiles, etc. It's exciting to delve deeper and find out why these connections exist. Great video as always.

  • Белый Герцог
    Белый Герцог13 timer siden

    NOlocal algorythm works very strangely today... Anyway, that's a cool video. o.o

    LUCKY DUCKIES13 timer siden

    Canale youtubicum tuum subscriptum est.

    LUCKY DUCKIES13 timer siden

    Habemus scientiam intelligentem.

  • Patrick Mugerwa
    Patrick Mugerwa13 timer siden

    I was waiting for something like: add this and that and that number you get is the devil's number.

  • Valentin Dimitrov
    Valentin Dimitrov13 timer siden

    Тhe information in this video would be very appreciated by Leonardo Da Vinci (the wisest polymath ever lived). Great Work!😉

  • Dakilang Maginoo
    Dakilang Maginoo13 timer siden

    I mean im gonna be honest, I watched the whole video, but I already lost it 2 minutes in the video.

  • A M
    A M14 timer siden

    Things do get nerdy around these parts. For a science subject: this one specific topic is very nerdy, the pattern talk. Holy moly. Very very nerdy. One truly have to have a very lively imagination.

  • President Skink
    President Skink16 timer siden

    That blow horn at around 18:53 startled me and the other 27 people in the restaurant...

  • Dingo Prod
    Dingo Prod17 timer siden

    Will have to watch it again coz i didnt get it :-/

  • Dmitry Grekov
    Dmitry Grekov18 timer siden

    Does anybody know, what are those local vertex rules he's talking about?

  • Ibad Ramadhan
    Ibad Ramadhan20 timer siden

    P S Y C H E D E L I C

    FRANCES LUNYOU20 timer siden


  • ayebrahletsksate
    ayebrahletsksate21 time siden

    is this how odd can be even?

  • Piyush Udhao
    Piyush Udhao21 time siden

    the thing is, my family is building a house, and im gonna ask my dad to get penrose tiling for the parking lot

  • Dhruv Shah
    Dhruv Shah22 timer siden

    Absolutely love what video compression does to the high-frequency patterns! Yes, my head hurts, but it's such a joy to watch something so simple break the compression algorithms.

  • WretchedGnat
    WretchedGnat23 timer siden

    Me being the nerd I am DnD dice.

  • MrPlumberguy23
    MrPlumberguy23Dag siden

    Ok hi af and ADHD and ADD go crazy

    HOOBA DOOBADag siden


  • Parasaurolophus Walkeri
    Parasaurolophus WalkeriDag siden

    My mind is so blown yet I understand none of this

  • Aria Hosseinzadeh
    Aria HosseinzadehDag siden


  • Jajou Fusade
    Jajou FusadeDag siden

    I... Don't know how I got here. I'm lost. I like it.

  • Michael Dower
    Michael DowerDag siden

    I'll be honest, i would purchase a booklet that has Penrose drawings and corresponding translucent paper and spend weeks trying to find the perfect angles for each of the different designs... and i think it would be a pretty neat replacement to wheres wally! if anyone finds anything like this, please let me know!!!

  • Evan Amies Galonski
    Evan Amies GalonskiDag siden

    Can you provide the source for the image of the Penrose pattern? I would love to print it out the transparency and try it out!

  • Vojtěch Kopecký
    Vojtěch KopeckýDag siden

    I'm glad, that someone has made a video about something from my country.

  • Atrocious Nightmare
    Atrocious NightmareDag siden

    Beyond fascinating.

  • Umashankar K
    Umashankar KDag siden

    I have to hear this another 50 times....😭 Probably I still don't think I could get this.

  • v1asec
    v1asecDag siden

    This is what I liked on Numberphile, except that your visual presentation is more refined. Thanks, a great video, perhaps one of the best I've seen. Makes me wish to tile my bathroom with 5-fold symmetry patterns. Well, next time, I guess :)

  • NikTalks
    NikTalksDag siden

    Johnny joestar be like : the golden ratio??.

  • chucktangy
    chucktangyDag siden

    So what are the rules for the vertices to keep the pattern working until infinity? And do those rules hold no matter the shapes (i.e. darts and kites vertices rules are the same for fat and skinny rhombus, etc)?

  • atorrent
    atorrentDag siden

    But have quasicrystals been found in a natural state / in nature? Does anyone know?

  • This is my LITE don’t block the SUN
    This is my LITE don’t block the SUNDag siden

    I disliked Prague

  • MGMaster Ov
    MGMaster OvDag siden

    My friend you forgot the circle for the platonic solid....

  • Reframer
    ReframerDag siden

    wow, what an interesting video! I like, when also historical facts are touched:) Well, the 5 within 0.5 of phi does not have anything to do with "five-ism" of phi. But you probably knew that, I just wanted to armchair quarterback xD

  • Seeky Unbounded
    Seeky UnboundedDag siden

    NOlocal compression didn't like that

  • Joshua Lee
    Joshua LeeDag siden

    So when do we discover Dilithium crystals, Scotty? Trek lore says a ton of quartz crystals are quasi crystals capable of powering antimatter generation...

  • Stevie-Ray
    Stevie-RayDag siden

    So Wang was Wong!

  • Meme Notlord
    Meme NotlordDag siden

    I live in prag

  • Diogo Cichocki
    Diogo CichockiDag siden

    The OCD hell look like this.

  • Artit Pongpira
    Artit PongpiraDag siden

  • MrGrevanar
    MrGrevanarDag siden

    So wait, is there a limit to the size of quasi crystals or not? Can you tile to infinity in 3d or only in 2d?

  • MrGrevanar
    MrGrevanarDag siden

    The curves on these tiles... do they repeat? I can't tell from the picture, but they seem to make an interesting pattern themselves.... Also, if I ever make enough money, I think I want this sort of thing as bathroom tiles...

  • Verlisify
    VerlisifyDag siden

    Me at 15:04 "Hey. No. Stop that"

  • Pavel navratil
    Pavel navratilDag siden

    mesmerizing how he make s 21 minute video abaut some shapes and numbers

  • Misu Satriyo
    Misu SatriyoDag siden

    Umm anyway, where can I get those transparent pattern paper thing?

  • Ramon Crespo
    Ramon CrespoDag siden

    The pattern is circular, the equation should look like a Mandelbrot set 4D representation

  • The Kaveman
    The KavemanDag siden

    That is a very powerful video , quite amazing in details and i don't think the story is finished here , i think it goes more sub atomic

  • Andy Pandy
    Andy PandyDag siden

    Mind blown!

  • monado550
    monado550Dag siden

    11:47 pun intended

  • s8chi
    s8chiDag siden

    How we think 1611 was: huhu i am smart The paintings: HAHA SAW THE HEAD FOR MEDICINE FOR HEADACHES

  • harro george
    harro georgeDag siden

    So many mentions of the golden ratio

  • Brigman
    BrigmanDag siden

    Maybe this is how universes work, in some abstract, obscure way. A multiverse laid out in a non-repeating pattern meaning we, as humans, could never use math to truly see what's out there, but yet the pattern of universes still exists.... just non-repeating.

  • Tom Liu
    Tom LiuDag siden

    Is this a conspiracy theory or what?

    SOURAJ RAHADag siden

    I wish I could understand all this..and feel smart about it...

  • Yong J
    Yong JDag siden

    2:05 I started getting SCP flashbacks from the background theme

  • kijkedwin
    kijkedwinDag siden

    Thank you, that is amazing..

  • The Entourage
    The EntourageDag siden

    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.

  • Patrick Hoesly
    Patrick HoeslyDag siden

    Mind blown! I need a lie down.

  • Aviation Hobbies
    Aviation HobbiesDag siden

    He is the new vsauce

  • Steven Glowacki
    Steven GlowackiDag siden

    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.

  • armondtanz
    armondtanzDag siden

    Ok, what hav i got to do right now in my life to understand thsi vid?

  • Somewhat Blank Paper
    Somewhat Blank Paper2 dager siden

    The hardest part is actually proving the conjecture lol.

  • Jacob Gould
    Jacob Gould2 dager siden

    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.

  • Nutthatch Wood
    Nutthatch Wood2 dager siden

    I need that big d20

  • soinhu foitu

    soinhu foitu

    2 dager siden

    This is at least a hint at why re-evolution is eternal sync-duration connectivity.

  • Awes
    Awes2 dager siden

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

  • soinhu foitu

    soinhu foitu

    2 dager siden

    Good job.. keep up the good work.?

  • çağatay tuncer
    çağatay tuncer2 dager siden

    my brain melted and I want to tile the whole house

  • Dan Z
    Dan Z2 dager siden

    uh huh

  • Fiesta_Blend458
    Fiesta_Blend4582 dager siden

    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

  • Mike O'Barr
    Mike O'Barr2 dager siden

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

  • Luxray Lloyd
    Luxray Lloyd2 dager siden

    Dam, Maths is so freakin cool!

  • Luxray Lloyd
    Luxray Lloyd2 dager siden

    I'm pretty sure i did something like that when I was a kid (it wasn't infinite, but I did try)

  • Breno Faria
    Breno Faria2 dager siden

    Why are people so confused? It's an interesting and clear message lmao

  • Professor Perry
    Professor Perry2 dager siden

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

  • Ayden Sibbern
    Ayden Sibbern2 dager siden

    Who else here's a child in the background? 10:31

  • tabaks
    tabaks2 dager siden

    1Password is leaps superior over LastPass.

  • DRakeTR of KBam
    DRakeTR of KBam2 dager siden

    This is the most intelligent illuminati confirmed video ive ever watched

  • 2Tri
    2Tri2 dager siden

    This is the most coincidence-filled thing I have ever seen in my life...

  • Релёкс84


    2 dager siden

    then you probably don't know what the word coincidence means...

  • Ofir Dolev
    Ofir Dolev2 dager siden

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