The Infinite Pattern That Never Repeats

30. sep.. 2020
8 793 848 Ganger

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 NOtown)
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”

    VeritasiumVeritasium3 måneder siden
    • Wtf does that mean

      Fudge A Tron GamingFudge A Tron GamingDag siden
    • I hate to break it to you, but infinite doesn't mean all, so there's no guarantee that any section on "pattern a" would appear on "pattern b". The patterns never run out of space to display the section, but they also never run out of alternate section to display in it's place.

      JayJay4 dager siden
    • @alnot01 Actually, Penrose was there first (meaning, he was the one who proved black holes must form under certain "benign" conditions that had been previously considered "unrealistic"). Hawking a bit later contributed to Penrose's singularity theorems.

      JanPBtestJanPBtest4 dager siden
    • I feel like they picked one thing but gave him a lifetime achievement Nobel. It was black holes because he was tacked on with the other winners. Either way well deserved.

      Bazza The GreatBazza The Great4 dager siden
    • I am from Czech republic 👌

      Daniel KomárekDaniel Komárek4 dager siden
  • Dear Kepler, Snowflakes are that way because hexagons are bestagons. - CGP Grey, probably

    Eli HaslageEli Haslage13 timer siden
  • Where can i buy the red, green and blue things?

    TyloreanTylorean13 timer siden

    Tushar MoitraTushar Moitra14 timer siden
  • This is an amazing video! The big boxes of these in the video would be really fun to play with - even for kids, I'd imagine. Especially, as educational tools. Did any find a good place to purchase kites and darts tiles?

    zeitblomszeitbloms15 timer siden
  • kind of like block chain tech

    Rich BuddyRich Buddy16 timer siden
  • I swear we all learn more in NOtown than school.

    Julian GarciaJulian Garcia19 timer siden
  • Work with V sauce?

    Dr .FosterDr .Foster19 timer siden

    Veronika ZoselovaVeronika Zoselova19 timer siden
  • You sure it doesnt repeat? I think people are quite simply too lazy to check

    Blas Felip HimmelreichBlas Felip Himmelreich20 timer siden

    Ashley the_gacha simpAshley the_gacha simp20 timer siden
  • Uhm.... I see a repeat in the thumbnail?

    Kaitlyn CunninghamKaitlyn Cunningham20 timer siden
  • My Girlfriend: buy some thing to eat Me :

    Ian FooIan Foo22 timer siden
  • “Why always six?” Cgp Grey:because hexagons are the bestagons

    Kurt PunzalanKurt PunzalanDag siden
  • I have a particular problem with 'unverifiable infinity' I would want to say that I don't believe the pattern is truly infinite.. So much as I think that it is able to build roated sub patterns into layers, where as it'd as likely take such an absurd scope to even find the repeat, that I think the comparison to shapes like squares, triangles, & even other multi-part shapes a bit on the unfair sense, as the building of the pattern uses logistical rules beyond 'fitting sides together'. Though, what i think is as likely as much else... it being rather unfair & .. sorta dismissive to say 'infinite number of patterns' while admitting to sub repeating parts. It's also 'slightly misleading' to suggest it's only 2 shapes that makes that pattern, when it ends up being dozens on dozens, with only 2 kinds. -- as if it was 1 pattern diced up into several, really.. Not to say 2 very simple elements of something can't make up something extensively more complicated then it's parts alone.. though, perhaps it's the secret right? that such things once weaved large enough becomes the fabric of which everything is made from.... and thus a thing onto it self where it becomes misleading to claim 2 elements once those patterns start creating patterns that create patterns & continue to do so the more that is pulled back out to a point of unknown stability. what of Protons & electrons? if woven so close & having it's own logic & laws, making up reality as we know it.. that the existence of everything else is just them.. might be missleading to say protons & electrons, when say.. you're holding a drink, or food. I do believe it is scale for sure and such things can lead to understanding about sheer fundamentals, but if the 'examples' are little more then utterly mind boggling & effectively impossible to examine in full with even projected future hardware, then... what of the real deal & why do we consider it immutable if at the core of thingss it is only a 0 or a 1... a fat shape or a shape, & by knowing what's what.. you could change the localized rules for x things, and manipulate the patterns. -- as any sufficiently complicated pattern would have a drift ability & in that excessive resistance to destruction via pattern changing. this being the whole of the thing... while localized patterns would have to change to fit the alterations.. while not changing the overall patterns.

    Kerns NoelKerns NoelDag siden
  • The special albatross morphometrically trace because list histologically knit anenst a acidic soldier. disgusted, plastic purpose

    Walter MooreWalter MooreDag siden
  • i don't know what tf they're talking about.

    Hydr0WavesHydr0WavesDag siden
  • I've learned so much but nothing at the same time

    TroveionTroveionDag siden
  • Poggers for God

    Keeva GraceKeeva GraceDag siden
  • I saw it repeat twice already

    kirby is a Christian mankirby is a Christian manDag siden
  • Excuse me

    Black BoardBlack BoardDag siden
  • My only question after watching this entire video: So, what sanitarium did Penrose end up in? (You just KNOW he's been drawing on the floor and walls of his room!)

    America just keeps getting greater!America just keeps getting greater!Dag siden
  • Thank you for using the phrase "raises the question" at 5:32 (which was the correct phrase to use in this instance), instead of using the phrase "begs the question" (which would've been the wrong phrase to use in this instance, since it means something entirely different)! I cringe every time someone misuses the phrase "begs the question!"

    ksmoker27ksmoker27Dag siden
  • I'm dizzy

    levirannlevirannDag siden
  • My eyes hurt

    IgnoredIgnoredDag siden
  • If it’s a “pattern” that doesn’t repeat, is it even a pattern?😂

    NJ_ 16NJ_ 16Dag siden
  • My mind is completely blown

    PrimePrimeDag siden
  • Snap!

    David PlenderleithDavid PlenderleithDag siden
  • Your comment at 19:43 encourages me to look closer at the Bible for physical, social and economic applications. Thanks.

    C GC GDag siden
  • Fun art fact: this wouldn't be a pattern this would be call a rhythm

    True dragon SlayerTrue dragon SlayerDag siden
  • i have never been so confused

    A_Aleta Jr. Glenn CliffA_Aleta Jr. Glenn CliffDag siden
  • after watching this video before sleep, i had a nightmare.

    Ho6Xc5Ho6Xc5Dag siden
  • How did I go from minecraft trolling to this anyways-

    Jophiel Philanna DeusvultJophiel Philanna DeusvultDag siden
  • 11:48 "It's futile" Nice Pun

    Night OwlNight OwlDag siden
  • Prague hmmm it is something I know but wait. Oh wait nvm it's main city of country I live in aka Czech republic. 😂

    Dejv 300Dejv 300Dag siden
  • Me:doesn’t understand 50% of the words Still me:understand everything

    XxshautyxXXxshautyxXDag siden
  • The most confusing game of Puzzle

    Vincent C. DicayananVincent C. DicayananDag siden
  • prog

    Haziq BaikHaziq BaikDag siden
  • 11:51 *Korega Requiem Da*

    Jahred GalanzaJahred Galanza2 dager siden
  • Yes

    Jahred GalanzaJahred Galanza2 dager siden
  • Jealous of that Celestron CGX in the background

    Andrew WhisenandAndrew Whisenand2 dager siden
  • This looks like something quilters could work out. LOL

    berngirl 56berngirl 562 dager siden
  • is that Juneau, AK at 2:55?

    Jim HoffJim Hoff2 dager siden
  • should i sub?

    Aidenlol bonzantoAidenlol bonzanto2 dager siden
  • no politician should be able to run for an office, unless they can memorize this talk-- ha ha -- no more politicians

    wonderful beeswonderful bees2 dager siden
  • too bad i have no clue what this is about, yet strangely interesting

    wonderful beeswonderful bees2 dager siden
  • Learned something

    Lazy TuberLazy Tuber2 dager siden
  • I understood most, and honestly it’s so beautiful. I love this kind of geometric mathematics. I’ve heard about phi before and I read a lot about the Fibonacci sequence and about the golden ratio in a book called “The golden ratio”. I loved this video and you have earned a sub!

    AreyouthickAreyouthick2 dager siden
  • Its so pretty

    Rook KolmRook Kolm2 dager siden
  • isn`t the circle a platonic solid as well?

    Master ofDeasaterMaster ofDeasater2 dager siden
  • 1:30 so dnd dice

    Y DY D2 dager siden
  • 9:43 the sound of pure glee

    Adelaide WattsAdelaide Watts2 dager siden
  • thank you Veratasium, very cool

    Daymian GamerDaymian Gamer2 dager siden
  • What my parents think when I’m on NOtown: he’s just watching silly videos What I really watch:

    Casual PlayerCasual Player2 dager siden
  • The instinctive brake assembly empty because tuba approximately perform afore a lazy stinger. impossible, flippant motorboat

    Roxanne LittleRoxanne Little2 dager siden
  • You know what? I actually understand all this

    AbdulRazaak PetersenAbdulRazaak Petersen2 dager siden
  • Thanks recommended

    VyldimVyldim2 dager siden
  • This is like mark robert but you didnt make anything just expalining stuff lol. But still this is so interesting

    PuryYT 5847PuryYT 58472 dager siden
  • This is like a conspiracy video on geometry.

    Meaty TofuMeaty Tofu2 dager siden
  • I have an uncle who is a crystollogist. I still have no idea what those spectral diagrams mean though.

    ganondorfchampinganondorfchampin2 dager siden
  • The loutish honey minimally pass because kilometer coincidingly scatter through a assorted custard. poised, trite breakfast

    MN ZENMN ZEN2 dager siden
  • Why aren’t my classes like this, this is actually interesting especially the way this guy explains it, it make me actually interested in the subject while my teacher explains things in gibberish

    Rhiyanna CRhiyanna C2 dager siden
  • "hexagon best tagons"

    Eavy EavyEavy Eavy2 dager siden
    • Does that mean that hexaflexagons are bestaflexagons?

      MikeRosoftJHMikeRosoftJH2 dager siden
  • brain hurts - will probably loose sleep off this

    Hannah LinHannah Lin3 dager siden
  • I think I have brain cells now

    shrekshrek3 dager siden
  • Shame it repeats

    Combine CoreCombine Core3 dager siden
  • You can EASILY find the repeating parts. Especially in the title

    ceiling gangceiling gang3 dager siden
    • No you don't. It's not about two little areas being the same, but that at some point the entire sequence repeats. Which it doesn't. Just like the number Pi has an infinite number of digits after the comma, and sequences like "1234" will occur multiple times, but it will never repeat.

      LeyrenLeyrenDag siden
  • Hexagon is the bestagon

    Josh VJosh V3 dager siden
  • I think that my brain cells have both melted and multiplied by watching this

    JackDoesGamingJackDoesGaming3 dager siden
  • Golden your telling me the secret to spin WAS IN A LITERAL PINROSE PATTERN

    Kaif IqbalKaif Iqbal3 dager siden
  • If the tiles don't repeat, then they don't form a pattern, right?

    Shayaan MorshedShayaan Morshed3 dager siden
    • That depends. Consider for example the number 0.12345678901234567890... - this is a number whose decimal expansion is periodic, and so it's rational (it's equal to 1234567890/9999999999). But obviously it doesn't contain all sequences of digits; for example, it doesn't contain the sequence 22. On the other hand consider the number obtained by concatenating all natural numbers: 0.1234567891011121314... . This is an irrational number; its decimal expansion isn't periodic. On the other hand there's an obvious pattern to it, and it has the following property: every finite fragment of it (and indeed any finite sequence of digits) eventually repeats (and so it follows that it repeats infinitely many times - but it cannot repeat periodically). What the video is saying is that the pattern is like the number 0.1234567891011121314..., not like 0.12345678901234567890... There is no finite fragment of the pattern such that the pattern consists of that pattern repeated indefinitely. On the other hand, given any finite fragment of the pattern, this fragment does appear elsewhere in the pattern, infinitely many times.

      MikeRosoftJHMikeRosoftJH2 dager siden
  • Me From czech republic- oh interesting

    JustPas1ngByJustPas1ngBy3 dager siden
  • I'm 10 and I liked this

    Aahza AkmalAahza Akmal3 dager siden
  • hi

    Aahza AkmalAahza Akmal3 dager siden
  • hexagons are the bestagons

    Trailers for DreamersTrailers for Dreamers3 dager siden
  • 1:58 omg i feel like im watching scp illustrated

    Sovi3tBoySovi3tBoy3 dager siden
  • Why no mask?

    Glitter flitterGlitter flitter3 dager siden
  • The disillusioned jail substantively mourn because reminder oppositely bruise aboard a cooperative minute. lush, quack hobbies

    Bethany MitchellBethany Mitchell3 dager siden
  • So panch tatva in Hinduism is real according to science.

    Chetan SounChetan Soun3 dager siden
  • The vengeful crown minimally please because actress exclusively raise below a dynamic fortnight. uncovered, clumsy peer-to-peer

    Diane ReidDiane Reid3 dager siden
  • will i ever understand this? absolutely not. will i continue to revisit this video as the years go by? of course.

    Alex NisaAlex Nisa3 dager siden
  • If it doesn't repeat then it's not a pattern.

    mwells219mwells2193 dager siden
  • What

    ChasaeChasae4 dager siden
  • The video that hooked me on Veritasium 🙂

    JCSViperionJCSViperion4 dager siden
  • I really love your speaking pace and style, very engaging.

    Rey TianeroRey Tianero4 dager siden
  • i have been braining so hard my think hurts

    Abdalrahman IrraiesAbdalrahman Irraies4 dager siden
  • Anyone else remember those little wooden shapes that were used in elementary school? I used to try to make perfect tilings of those little shapes and I swear that I used to take the fat rhombus and the thin rhombus and make those little patterns all over my desk. I never knew that 7-8 year old me was apparently making penrose patterns for fun, I just wanted to make perfect little patterns out of every wooden shape, no matter how hard it was

    Amanda SlocombAmanda Slocomb4 dager siden
  • Why does this looks like a 8 year old video even tho it’s like 3 months old

    Rick RollRick Roll4 dager siden
  • Illuminati confirmed

    Random IzerRandom Izer4 dager siden
    • actually, it is nature confirmed.

      RayRay 2021RayRay 20212 dager siden
  • can u do my math for me

    DarkoDarko4 dager siden
  • Math Teacher: the test isnt hard. The test: 0:01

    LeoLeo4 dager siden
  • Another segment I call “I could have lived peacefully without knowing this and always thinking about it”.

    YuYu’s PropertyYuYu’s Property4 dager siden
  • Bro it's not a pattern of it doesn't repeat

    Aramus DayAramus Day4 dager siden
  • That means it’s not a pattern then a pattern repeated it’s self

    Link_the_proLink_the_pro4 dager siden
  • But isn't the definition of pattern something that repeats..?

    Eric ColemanEric Coleman4 dager siden
  • robert burger

    Zeus But shavedZeus But shaved4 dager siden
  • "never repeats" yet it clearly does.

    Caleb VentimigliaCaleb Ventimiglia4 dager siden
  • what, I have no idea what happened, am I supposed to understand this or is it non comprehensible?

    Umbro the UmbreonUmbro the Umbreon4 dager siden
  • omg dude this is so crazy and impressive

    United StatesUnited States4 dager siden
  • A wise man once told me that hexagons are the bestagons

    Aquasphere4Aquasphere44 dager siden