The Infinite Pattern That Never Repeats

  • Publisert 23 dager siden

    Veritasium

    Runtime: 21:11

    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: 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 NOsection)
    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
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”

16 dager siden
Behrang Saeedzadeh
Behrang Saeedzadeh

The subject deserves a video IMHO.

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touristguy87
touristguy87

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

5 dager siden
Flick Penrose
Flick Penrose

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

5 dager siden
KyrilPG
KyrilPG

@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 : https://maps.app.goo.gl/cWiLsroPSjUFHzwq6 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.

6 dager siden
Pranav Pothanis
Pranav Pothanis

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 🇮🇳🇮🇳

6 dager siden
ZB. mochi
ZB. mochi

BOOM! IM SMART NOW jkjk Nop

17 minutter siden
ZB. mochi
ZB. mochi

But this was pretty interesting:)

16 minutter siden
wilson plays
wilson plays

Prague reminds me of the honest guide

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Mrf AK
Mrf AK

@9:41 kekule patterns!

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Behrang Saeedzadeh
Behrang Saeedzadeh

Isn't it easy to create never repeating patterns algorithmically?

3 timer siden
Maher Louis, PE, PEng.
Maher Louis, PE, PEng.

Dear Young Man, Your approach for understanding is misleading you. There is a science called Crystallography which clarifies there are seven crystal systems: triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. If you educate yourself referring to basic sciences, surely you will safeguard yourself from a lot of troubles

6 timer siden
Stephen Daire
Stephen Daire

(Al-Pd-Mn) quasicrystal surface. https://en.wikipedia.org/wiki/Quasicrystal

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Enrique Rodriguez G
Enrique Rodriguez G

I uh.. dont know why YouTube brought me here

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formdoggie5
formdoggie5

...if it doesn't repeat it's not a pattern, by definition. The title doesnt make sense. All this does is show how things that arent patterns, aren't. You're proving a non-sequitur and then acting surprised/amazed its acting precisely in that fashion.

7 timer siden
formdoggie5
formdoggie5

@Релёкс84 patterns are numeric or shape progressions or sequences that repeat themselves, by definition. Unless they've changed the definition since I went to school. If it doesn't repeat itself, it's not a pattern, by definition.

3 timer siden
formdoggie5
formdoggie5

@Релёкс84 1 2 3 4 is a pattern with the "add 1" repeating itself.

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Релёкс84
Релёкс84

Please provide a definition of a pattern that states it cannot repeat. In the mean time, 1, 2, 3, 4... is not a pattern?

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Im Mes
Im Mes

can you make a lot of girlfriends explaining them that (NOT MATHEMATICIAN GIRLS I PRECISE)

8 timer siden
Declan Techo
Declan Techo

For myself Angles of thick rhombus: 72 & 108 Angles of thin Rhombus: 36 & 144

8 timer siden
anTyfolium
anTyfolium

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

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Filipe Lima
Filipe Lima

Math is AMAZING!

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Pablo
Pablo

just stunning

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True Indian
True Indian

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!!

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Geomegic DIY Coloring Pages
Geomegic DIY Coloring Pages

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

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yasio bolo
yasio bolo

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

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Wafikiri
Wafikiri

I have found an infinite number of infinite periodic 2D-tilings of equal regular pentagons and half as many equal same-side-as--pentagons 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.

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yasio bolo
yasio bolo

these connections exist. Great video as always.

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Telavus
Telavus

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

15 timer siden
Madalyn Rogers
Madalyn Rogers

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

15 timer siden
Rick Lennox
Rick Lennox

🤯

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The Meme Man
The Meme Man

The infinite comment that never repeats.

16 timer siden
Jalen MichalsLevy
Jalen MichalsLevy

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)

16 timer siden
Çağrı Bıkmaz
Çağrı Bıkmaz

Nice content

16 timer siden
The Duck
The Duck

is that really a pattern if it never repeats

17 timer siden
Релёкс84
Релёкс84

Why wouldn't it be?

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Silvio Francisco
Silvio Francisco

Wow!! Unbelievable! I have no words!

17 timer siden
Georgescjh
Georgescjh

Greetings from Prague !

17 timer siden
Nidhogg vom Walde
Nidhogg vom Walde

When I design the next bathroom....

18 timer siden
Devin O'Driscoll
Devin O'Driscoll

Ultra Jurable Steel @ 19:17

18 timer siden
Mason Hunter
Mason Hunter

Robert’s nonperiodic tiling looks periodic

20 timer siden
OXMOND Tutorials
OXMOND Tutorials

Beautiful! 🤓👍🧡

20 timer siden
John Smith
John Smith

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 ....

21 time siden
Daniel Amaral
Daniel Amaral

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.

21 time siden
Белый Герцог
Белый Герцог

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

21 time siden
LUCKY DUCKIES
LUCKY DUCKIES

Canale youtubicum tuum subscriptum est.

21 time siden
LUCKY DUCKIES
LUCKY DUCKIES

Habemus scientiam intelligentem.

21 time siden
Patrick Mugerwa
Patrick Mugerwa

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

21 time siden
Valentin Dimitrov
Valentin Dimitrov

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

21 time siden
Dakilang Maginoo
Dakilang Maginoo

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

21 time siden
A M
A M

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.

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President Skink
President Skink

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

Dag siden
Dingo Prod
Dingo Prod

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

Dag siden
Dmitry Grekov
Dmitry Grekov

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

Dag siden
Ibad Ramadhan
Ibad Ramadhan

P S Y C H E D E L I C

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FRANCES LUNYOU
FRANCES LUNYOU

WHERE CAN I GET THOSE [[KITES & DARTS]] THAT YOU MADE FROM PLASTIC??? I WOULD LOVE TO HAVE THEM TO TRY TO MAKE A QUILT FROM THOSE PIECES...... BLESSINGS & BE HOPE FILLED FRANKI LUNYOU

Dag siden
ayebrahletsksate
ayebrahletsksate

is this how odd can be even?

Dag siden
Piyush Udhao
Piyush Udhao

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

Dag siden
Dhruv Shah
Dhruv Shah

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.

Dag siden
WretchedGnat
WretchedGnat

Me being the nerd I am DnD dice.

Dag siden
MrPlumberguy23
MrPlumberguy23

Ok hi af and ADHD and ADD go crazy

Dag siden
HOOBA DOOBA
HOOBA DOOBA

POGERSSSSS!!!!!!!!!

Dag siden
Parasaurolophus Walkeri
Parasaurolophus Walkeri

My mind is so blown yet I understand none of this

Dag siden
Aria Hosseinzadeh
Aria Hosseinzadeh

noice

Dag siden
Jajou Fusade
Jajou Fusade

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

Dag siden
Michael Dower
Michael Dower

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!!!

Dag siden
Evan Amies Galonski
Evan Amies Galonski

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!

Dag siden
Vojtěch Kopecký
Vojtěch Kopecký

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

Dag siden
Atrocious Nightmare
Atrocious Nightmare

Beyond fascinating.

Dag siden
Umashankar K
Umashankar K

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

Dag siden
v1asec
v1asec

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 :)

Dag siden
NikTalks
NikTalks

Johnny joestar be like : the golden ratio??.

Dag siden
chucktangy
chucktangy

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)?

Dag siden
atorrent
atorrent

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

Dag siden
This is my LITE don’t block the SUN
This is my LITE don’t block the SUN

I disliked Prague

Dag siden
MGMaster Ov
MGMaster Ov

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

Dag siden
Reframer
Reframer

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

Dag siden
Seeky Unbounded
Seeky Unbounded

YouTube compression didn't like that

Dag siden
Joshua Lee
Joshua Lee

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

Dag siden
Stevie-Ray
Stevie-Ray

So Wang was Wong!

Dag siden
Meme Notlord
Meme Notlord

I live in prag

Dag siden
Diogo Cichocki
Diogo Cichocki

The OCD hell look like this.

Dag siden
Artit Pongpira
Artit Pongpira

https://www.youtube.com/watch?v=0UiEdg8P5iw

Dag siden
MrGrevanar
MrGrevanar

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?

Dag siden
MrGrevanar
MrGrevanar

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...

Dag siden
Verlisify
Verlisify

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

Dag siden
Pavel navratil
Pavel navratil

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

Dag siden
Misu Satriyo
Misu Satriyo

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

Dag siden
Ramon Crespo
Ramon Crespo

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

2 dager siden
The Kaveman
The Kaveman

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

2 dager siden
Andy Pandy
Andy Pandy

Mind blown!

2 dager siden
monado550
monado550

11:47 pun intended

2 dager siden
s8chi
s8chi

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

2 dager siden
harro george
harro george

So many mentions of the golden ratio

2 dager siden
Brigman
Brigman

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.

2 dager siden
Tom Liu
Tom Liu

Is this a conspiracy theory or what?

2 dager siden
SOURAJ RAHA
SOURAJ RAHA

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

2 dager siden
Yong J
Yong J

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

2 dager siden
kijkedwin
kijkedwin

Thank you, that is amazing..

2 dager siden
The Entourage
The Entourage

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.

2 dager siden
Patrick Hoesly
Patrick Hoesly

Mind blown! I need a lie down.

2 dager siden
Aviation Hobbies
Aviation Hobbies

He is the new vsauce

2 dager siden
Steven Glowacki
Steven Glowacki

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.

2 dager siden
armondtanz
armondtanz

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

2 dager siden
Somewhat Blank Paper
Somewhat Blank Paper

The hardest part is actually proving the conjecture lol.

2 dager siden
Jacob Gould
Jacob Gould

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.

2 dager siden
Nutthatch Wood
Nutthatch Wood

I need that big d20

2 dager siden
soinhu foitu
soinhu foitu

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

2 dager siden
Awes
Awes

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

2 dager siden
soinhu foitu
soinhu foitu

Good job.. keep up the good work.?

2 dager siden
çağatay tuncer
çağatay tuncer

my brain melted and I want to tile the whole house

2 dager siden
Dan Z
Dan Z

uh huh

2 dager siden
Fiesta_Blend458
Fiesta_Blend458

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

2 dager siden

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