## 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: 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 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

## Kommentarer

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

## 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 : 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.

## 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

## 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?

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

Math is AMAZING!

just stunning

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!!

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

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

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

## 5 timer siden

these connections exist. Great video as always.

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

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

🤯

The infinite comment that never repeats.

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)

Nice content

is that really a pattern if it never repeats

Wow!! Unbelievable! I have no words!

Greetings from Prague !

When I design the next bathroom....

Ultra Jurable Steel @ 19:17

Robert’s nonperiodic tiling looks periodic

Beautiful! 🤓👍🧡

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 ....

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.

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

Canale youtubicum tuum subscriptum est.

Habemus scientiam intelligentem.

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

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

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

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.

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

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

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

P S Y C H E D E L I C

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

is this how odd can be even?

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

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.

Me being the nerd I am DnD dice.

Ok hi af and ADHD and ADD go crazy

POGERSSSSS!!!!!!!!!

My mind is so blown yet I understand none of this

noice

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

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!!!

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!

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

Beyond fascinating.

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

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 :)

Johnny joestar be like : the golden ratio??.

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)?

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

I disliked Prague

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

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

NOlocal compression didn't like that

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

So Wang was Wong!

I live in prag

The OCD hell look like this.

nolocal.info/have/video/ZYedecignYhsza4

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?

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...

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

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

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

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

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

Mind blown!

11:47 pun intended

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

So many mentions of the golden ratio

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.

Is this a conspiracy theory or what?

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

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

Thank you, that is amazing..

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.

Mind blown! I need a lie down.

He is the new vsauce

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.

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

The hardest part is actually proving the conjecture lol.

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.

I need that big d20

## soinhu foitu

## 2 dager siden

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

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

## 2 dager siden

Good job.. keep up the good work.?

my brain melted and I want to tile the whole house

uh huh

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

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

Dam, Maths is so freakin cool!

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

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

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

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

1Password is leaps superior over LastPass.

This is the most intelligent illuminati confirmed video ive ever watched

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...

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