# 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 NOworld)

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”

@DeathMark recording channel no just non-spinning black holes.

Wait...did Penrose even know how to extract energy from a spinning black hole?

when you make the pattern seen at 10:04 and 12:26 as your home wallpaper, it creates interesting lines when you swipe to multi-task and back home, what's up with that?

@ShadeyBladey you don't have enough passwords.

@touristguy87 I don't need any program to remember my passwords. >:8o

this guy literally turns math into a conspiracy theory

Other people: I watched netflix, I watched an episode of bleh bleh bleh Me: I watched a video about infinite tiling Owo AND IT WAS PURE AWESOMENESS UWU

PRAGUE was built by the rich selling the poor as slaves to Arabs..fun fact??

what?

couldn't you just add one more dart or kite to that tiling and throw off the fraction equally the golden ratio?

Right, I'm gonna head to bed

I’m confused what is this pattern called and how does it relate to the multiverse?

all of those 0.5s are just a specific numerical representation of the value 1/2, and have no connection to the number 5.

Me : *reads title* Also me: u wot m8

What

aspect ratio of the video is 1.618. The Golden Ratio. That's hilarious!

another masterpiece from penrose..

so is it a pattern?

I am watching it for the second time to understand it better

You use a few tiles, it's futile.

8

is this lesson 5?

Did I get it? No. Did I enjoy it? Yes.

A non repeating pattern is an oxymoron. A pattern by definition needs to repeat, therefore there is in fact no such thing as a non-repeating pattern. If it doesn't repeat, it is not a pattern. Sorry dude.

Is our brain only a processor and when we take acid, the patters, aka the math that our conciousness really is, shines through?

class: shapes are for kids. veritasium: are you challenging me

i like your funny words magic man

Would it be possible to use Penrose pattern numbers as a template for cryptographic functions?

This is way more fun than math class!

How can people see all of these perfect patterns in math and in the world and say it was a random accident and not a planned creation

Does this mean the Keppler's Conjecture proves that some things are just obvious truths

For those of you who didn't notice, the aspect ratio of this video was a little... weird. Veritasium uploaded this video at a resolution of 1748x1080. Divide 1748 by 1080... The aspect ratio of the video is 1.618. The Golden Ratio. That's hilarious!

For some reason I knew that number would show up.

Why is the aspect ratio so weird

Off topic, but would a four-dimensional being be able to see the whole pattern?

And this all started because someone started overlaying hexagons

this is a 20 minutes of matematical beauty orgasm

9:36 I will pay real money to get that transparancy set you were playing with.

One of the best sleep lullaby

Interesting and very very informative videos!!!☺️☺️ Who agrees??

0:19 visit germany and you will change your oppinion xD

the kites and darts also are similar to the rhombi, the rhombi can actually be used to make the kites and darts. You place the skinny one over the big one so that the long diagonal of the small one overlaps the fat one, and matching of the corners that the diagonals that overlap. you can then use one of the two connecting pairs of edges on the small rhombi to divide the fat rhombi into a single kite and a single dart.

Seriously watching this after my work, my head hurts. You might have found another way of making people head hurt :-)

how can someone even know that my country exist?

Never doesn't exist.

Did anyone else got a bit aroused?

I've just watched the Royal Institute vid on these tilings hosted by Penrose himself, and I've realized why "Justice Cap" sounds weird. It's because he was actually saying "Jester's Cap" the entire time. Now THAT name makes a lot more sense.

Yes infinity exists, it's amazing :D

very interesting

Me at 9:03: "When a grid's misaligned with another behind that's a moiré" (thanks xkcd)

This was beautifully made. Thank you.

🤯 awesome!

WHERE IS YOUR MASK!? 2020 sucks.

the golden ratio part was unnecessary.. just when i thought ok i guess the videos over... put me in another twist of thinking.

Yep. He's got all the dice he'll need. Ready for some D&D.

oxymoron video title you cannot have a pattern that never repeats given that a pattern is a series of repetitions short... click bate and back in the day pluto was considered a planet unlike today so this theory has flaws

@Релёкс84 the repetitive pattern is the radix rules like you said your not familiar with what I'm saying. please google it

@devilzwishbone2013 I have no idea what you're rambling about or why you mentioned base 10 or base 2. All I did was mention two sequences: 1234567891011... and 1101001000100001... Both of these have nothing to do with each other, the only important thing about them is they never repeat, so according to you they are not patterns. That's all I'm saying and nothing more.

@Релёкс84 big flaw in your logic in that the pattern is repeated, its called radix ruling * each number is unique * each symbol is unique * highest unique symbol is base-1 what you have done is compared 2 different number bases as being the same base 10 (decimal or denary) with base 2 (binary) had you of stated that 10 is not the same as 10 using only the base 10 numbering system then your point would of been valid but you went from one pattern set to another and tried to argue it as the same please don't confuse abstracted thought with pattern repetition

Back in Kepler's days? Think a bit harder. Also, I guess 123456... and 1101001000100001... are not patterns according to you.

I feel like these could link to the fourth dimension

The original thinkers/scientists MUST have been into hallucinogenics. That`s the only way I can aim to understand the content of this video. Very interesting.

So if a plane is homeomorphic to an R² [0;1) unit square does that mean that if you construct a *large* plane out of *uncountably many* such squares conjoined side by side each tiled with a different penrose mosaic, such a *large plane* would contain all of *The* Penrose tiling?

@Релёкс84 You cannot tile a plane like that, I was suggesting to construct a topology object similar to a plane but consisting of an uncountably many unit squares. Just like an Alexandroff line but for 2D

I'm really curious to know how you're planning to tile a plane with uncountably many squares.

"it's fuTILE" 11:49 i died

Since Simone Giertz callender

This video is kinda related to the discovery of Quaiscrystals. Nobel Prize-Discovery of Quasicrystals: physics.aps.org/story/v28/st14#:~:text=Overall%2C%20the%20symmetry%20of%20the,forbidden%20for%20any%20periodic%20crystal.

2:15 damn, those shapes look like the oreo meme

5th Church: 👀

I want a penrose quilt

ok

18:18 he mentions a "rules for the vertices" so you can't make a mistake in pattern. Does any one know them? :)

My mind has been blown but I'm not quite sure how.

You should sell tiles. I bought a set on Etsy but they only tile about a square foot.

This is amazingly mind-bending. I love this channel.

Bees: Catch up, humans.

🤯

Very interesting. Crystal formation, electromagnetism and gravity are phenomena that defy rising entropy of the universe.

I still can't get my mind around this

I feel like this is a conspiracy

Incredible, then people talk how everything just came into existence by accident. There us bo way that something so perfect existing everywhere in nature is not designed.

My Eyes Be Like O-O

ars of training in mathematics and I just watched this video and drooled in utter confusion

It is very complicated

Superb video, so wonderfully explained and the visuals were absolutely brilliant. 👏🏻👏🏻👏🏻

I’m gonna pretend that I know exactly what he’s talking about

H

Knowledge Is Power noworld.info/video/video/xHTWgc9918a3pJo.html&ab_channel=GleebGliberGalacticaGavorti

Bus seats be like:

Well he won Nobel Prize.👍

Intelligence +1

So satisfying. Have you talked about the dragon curve? I’d love to hear your thoughts on that. “It’s right up your alley” -Jurassic Park reference ahoy

Imagine someone watching this who is color blind

They still see it as different shades of B/W, even if colour blind means 'no colour perception at all'

Bruh i need to get higher to understand this

this is the next Vsauce

OK too late for me to try and watch this, but riddle me this, isn't a pattern by definition something that repeats? I mean a "pattern that never repeats" sounds like an oxymoron. Or is that the whole point here?

Absolutely fascinating. I recall a quote, “Mathematics is the language in which God has written the universe,” and it's things like this that constantly reinforce the sentiment. I watched a documentary a while ago about mathematics in nature and architecture. One of the most interesting aspects of it was the discussion about the golden ratio, largely focused on its role in architecture. That such a prevalent aspect of architectural design is the keystone to an intrinsic quality of this edge case of geometric possibility makes me wonder about the ability of the human subconscious to divine the underlying structure of reality.

It is, the pAtterns are repeating in a messy way

I have ocd and this is disturbing me

Wait so all the dice in dnd are Platonic solids

close packed cubic is also close packed hexagonal.. a 90° rotation shows 6 sides of a cube... carbon crystal from Brazil.. black diamond.. with natural tesseract pin.it/4T7HXhS

once upon a time.. I was just married and I picked up a Scientific American at the grocery store.. I found an article about Penrose tiles... I put down the magazine and cut a bunch of the tiles.. I spent a few minutes trying to create a semi periodic arrangement.. they also make periodic symmetry.. so I looked at the picture... and my tiles, and it looked like if I marked one side of each type of tile, I would be able to predict which tiles came next.. took about 15 minutes.. I finished the article and read the good doctor Penrose took more than 20 years to figure it out... I have no degrees.. I love mathematics and science... that's the one and only Scientific American I have ever bought. .. I am a long time member of the AAAS and get most of the science I spout from my father and Science magazine where serious scientists publish their work for peer review.. and I read.. a lot... I have a laboratory, and a homemade electron microscope.. among other things.. Black holes are the result of a finite universe begun with a bang... so are all the other more recent science available at universities across the Planet.. if one doesn't teach BB theory one does not teach physics in America... the problem is.. the expansion of our Universe appears to be accelerating.. which is like throwing a ball and watching it accelerating away from your hand... clearly impossible... it's the reason why we are taught the "second law of thermodynamics".. which says all systems devolve over time to become less organized... fortunately.. it's not true.. we live in a Universe that is infinite in both Time and Space... and it gives a different starting point for all our measurements... it eliminates many of the infinities encountered in the relativity equations.. and.. it allows Feynman's math to work with no normalization.. or re- normalization.. whatever that is.. he re normalized.. to make observations fit in a closed universe... it's not.. and I really don't think black holes are a necessary ingredient for an infinite Universe.. but since I just figured it out.. I have not had a chance to make observations myself.. it's a very necessary ingredient to understanding the Universe we live in... books give information.. but it is not necessarily true there's a lot we don't know.. BB universes, and other types of mass hypnosis from television that create blinders on people.. even the smartest people.. we only have the information available at the time... A Einstein said we stand on the shoulders of greatness... to see just a bit further down the road peace y'all StarFire Family Industries Starfirediamondmines@gmail.com Richard Carew..and Dr Punkin Pie Carew.. phdoodly do dog.. the best lab partner ever ☆☆☆ ya know that missing mass and dark matter and energy?.. like BB universes.. it's magic, not science.. if you don't see the math it's not science pin.it/6FEMhUp the StarFire Family wishes you Peace and Prosperity Ad Infinitum 🙏 Peace ✌☮

Feels like 8 grade class, right after skipping 3 previous lessons.

What practical application does this have in real life? >:8o

I have an AD&D d30 from the '80s. >:8o

My brain just ooozed out my ears

sam o nella moosic

I said a bad word when phi came up.

wear a damn mask bro

*Tool likes this*

Medieval era islamic tile artists were doing this tiling way before Penrose "proved" it...fascinating confluence of art and mathematics.

very intresting.