The Infinite Pattern That Never Repeats
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- Опубликовано: 20 май 2024
- Simple 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 RUclips)
Animations by Ivy 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”
Congratulations to him, he genuinely deserves it!
Hi
This video triggered everything inside of me
Roger penrose was a close friend and research partner of stephen hawking.....he totally deserves it
Was this planned by you to time it with the announcement?
I’d like to point out this dude hated his professor so much, he looked at 20,000 squares just to prove him wrong
@@AmeshaSpentaArmaiti its a joke dude...
@@AmeshaSpentaArmaiti learn what a joke is
@@kirbydied2875 learn what critical thinking is. Critical analysis is not necessarily irreconcilable with humor. In fact, I thought his second sentence's observation was funny.
Ight
@@AmeshaSpentaArmaiti not serious replies offering an alernative unfunny punchline for the joke, I mean, who wants an unfunny joke? That's just not helpful.
All I was thinking throughout this whole video was:
"I have to remember this when I'm tiling my bathroom in my house when I'm older"
Lol
I'll help u do that
Yes, same. It'd be quite intriguing to pull it off and still look fairly cool
dont bother, it would just be fu-tile...
(hey, he said it in the video, dont blame me for the bad pun)
RIGHT?! XD
They've recently discovered a single tile that accomplishes the same thing on its own! Would love to see this revisited.
It is a 13-sided hat shape. It looks like the black Jamiroquai hat. I can’t wait to see a video about that either.
Damn, you beat me by two whole days. I only just learned about the 'einstein' tile (not named after famous physicist, but merely the fact that it requires only 1 'stone' [tile]).
Came here for the same reason
Yes! That's why I'm here again
YES
I'm from Czech Republic and let me tell you - I feel so so happy anytime any random person on the internet mentions our country! We are quite small and don't get mentioned too often!
I'm from Czech to and I feel the same
The feel of any random country from Latam...
I Don't Think so I have heard of Czech Republic many times. Mainly on the cover of Classmate(Indian Notebook Brand) Notebooks Mentioning about the beauties of Czech Republic and how important it is to Europe Mainly about a city known as 'Prague'. The Aim of the cover pages is to convey different sort of informative info and helps brand gain attention. But this country is their. I thought it was a small country with high significance in tourism.🙂
as someone who plays geoguessr I see it all the time 😂
Me: Gives this pattern to the guy tiling my kitchen
Tile guy: Sweats profusely
👽👍
Worst yet would hear him say: "Alright, I'm done"
...and he just created a singularity in you kitchen
His brain divides by zero.
I saw this comment already!
@@nemo4555 i think if you purposely create a specific singularity in the tiling you prevent the crystal from failing at distance... i think. Theres this wierd decagon shape you can make that forces the tiling to do wierd things.
“Wang’s Conjecture was false.”
Me, through a mouthful of chips, not understanding a word of this: “Haha, what a loser.”
HAHAHAHAHAHAHA
hahahahha
"He forgot to incorporate gravity, i was wondering why he didnt do that" ~Brian Regan with bag of Cheetos
This made me laugh out loud a lot 🙌🏽
You no mess with Lo Wang
While studying symmetry in school, I felt it was a boring topic
And now here comes this guy who's making every possible boring topic interesting
You're just AWESOME!
Him: it's not that complicated.
*Proceeds to explain the 4th dimension*
Had some crazy flashbacks of being back in school making those same patterns with wooden shapes. Pretty cool.
It is a boring topic, repetitive too; after you learn the first half, you sit through and learn the second half which is basically a mirror image of what you already learned.
Geometry has ALWAYS been a (potentially) fascinating topic, and it's a sad reflection on our way of doing education that generations of people have found it otherwise.
Just right now they found the first single tile that tiles the plane aperiodically, calling it "eistein". Amazing breakthrough! It does however require mirroring
Einstein, German for "one stone",
the latest variant found (in or before summer 2023) is called Spectre (not the Bond movie)
They found a variant which doesn't require mirroring also too!
@@fishxw That's awesome!!! Amazing how geometric discoveries are still being found today
Cool!
I feel like i learnt alot while learning nothing at the same time
Just like school
The best way to describe it is learning a lot of useless information
Same
@@RAHHHSCREWYOU yeah i was just joking
or was I?
*Vsauce music plays*
DITTO
Imagine finding over 20,000 tiles so that you could prove your professor wrong
Yup XD second reply ez
the pure spite is respectable
Yup XD fifth reply ez
Yup XD seventh reply ez
the things students can do out of spite
Your visualisations are stunning. Such intricate patterns, drawn so beautifully
Huge thanks for this!!! I love these mathematical/geometric/pattern discussions. My absute fascination was engaged.
I want a Penrose tiling set!
By the way, I'm 67, nearly failed my maths 'O' level, ended up trading as a teacher, did an extra maths course after my degree, and became a maths and art specialist (primary - UK). Taught kids tables by using patterns, and colouring them. One class of mine shocked an OFSTED inspector because around half of the kids said maths was their favourite subject..... all because of pattern in maths. And it was all started by my fascination with Fibonnaci (amongst other mathematical patterns)
Builder: So what kind of tiles you want in your bathroom then?
Veratasium: Well....
Underrated
bore off
wouldnt that be the ultimate ocd trigger?
i read that as Veritaserum-
@@starryeyedgirls I see your from the sua too lol
great video; I've been looking for rigorous but recreational math content like this on RUclips for years!
Today I randomly saw a short showing aperiodic monotile and immediately came back to this video. It is so fascinating to some widely accepted opinion (minimum 2 shapes are required for aperiodic tiling) change
Now only one shape is required for aperiodic tiling
This reminds me of an old saying we have here: "Everyone said that it was impossible. Then someone came who didn't know that and just did it."
Ikr
Pretty much the speedruning community in a nutshell honestly.
Or in other words, it seems impossible uniting it done?
Kinds like the fandom and the tollbooth
@@prajuktadeyy nothing is impossible UNTIL it's done?
Like the PHANTOM tollbooth?
:D
6:10 The ultimate smartass student, all raising his hand like: "Um, professor? I found 20,426 examples of how you're wrong."
katie kawaii lol
he found 1 example, which required 20,426 tiles, which might be just as annoying "I found this 1 specific example involving 20,426 unique tiles showing that you're wrong"
he should be put into hope peaks academy for being an ultimate
LMAO
He got nothing to do and he started to connect things to find something
The quality is so high. It's like a documentary teachers show you in class if there is spare time except more interesting and more brain-expanding. -sincerely Uel
I love the video. It’s really astounding how you are capable of explaining it in a way that makes it sound easy and fun to explore. Also, at 09:40, during the pattern overlap, I could have sworn a saw a face looking at me. I might be haunted….
“Well it’s infinite, so it’s gotta repeat at SOME point, right?”
Scientists: “lmao no”
there's parts that repeat but the whole thing won't appear twice next to itself / ex. 50% is some structure and the other 50% is that structure, or ex. you have 4 25%s and all 4 are the same thing.....there's lots of randomness
@@stevenmathews7666 What he said then :)
You will never find a pattern, as big as it is (even infinite), that will repeat !
This video was so crazy ! So good :)
I don't understand though why any part of those patterns could not be part of the same one infinite pattern. Since it never repeats itself and is infinite, it means that any arrangement we see could be / is part of the flat out infinity of those arrangemnts.
@@Miniclash What you said is indeed possible, it's the same thing that Steven said. Yes you can have small patterns that repeat themselves, but that's not what the video shows. The video tells you that you won't ever be able to find a unique recurrent pattern that you could translate and create a bigger pattern with. There has to be only one pattern that fills the entire space.
@@camstudiosfrmd8 I'm trying _extremely_ hard to understand this, and I feel like I'm close to understanding. It's just so confusing
*Deep Inhale*
I didn’t need an existential crisis about pentagons.
They solved it. Pay attention.
Roland Duson they made a joke, pay attention.
@@LordLongHands You're so boring and typical.
*Deep Inhale*
Science says otherwise.
@@Below-Zero. it's more boring and typical to miss the joke my friend.
Ive never said this in my like, 10 years if watching youtube, but I wish I could pay you for making videos this good.
an aperiodic monotile was just found!!!
Wonder if he will do a follow up video!
*Something happens*
Golden ratio: hello there
GENERAL RATIO!
You are a bold one
This video's aspect ratio
e & pi together with phi, looking at the sofa constant
The angel from my nightmare
@@jmir1 Sadly not, would be sooo amazing if it was though
"daddy, what do you do?"
"I look at shapes"
"That sounds easy"
"Well I also look at colours!"
??? I don’t get it
well that throws a wooden shoe into it.
@@trystankitty5393 you didn’t watch the video??
Yes daddy.
@@carolinesmercantile4290 and matches
Whenever I watch a veritasim infinite math video it feels like my soul is being lifted into a totally different universe of interconnecting math. Super great videos.
The Einstein Tile has been found!!!! Someone tell this man to do a follow up video.
I’m gonna pretend that I know exactly what he’s talking about
Golden ratio
Most impressive and acceptable theory explanation
ruclips.net/video/DIrvM1gcnPU/видео.html
Sarath chandran thanks I’ll watch it later if it’s not a rick roll lol
wait an i actually smart or sum cause i mostly understand nah it's probably just cause it's 3 in the morning my brain is extending
As good a place as any to start.
@@paulembleton1733
ruclips.net/video/-tabN6Z385w/видео.html
Imagine having Penrose tiling in your bathroom floor. It's a very cool pattern, it'd be great to look at while you're otherwise occupied.
SHITTING YOU MEAN
I'd stare at it until my bum was dry
"I didn't do my homework the floor was too interesting"
I want to retile my entire bathroom now.
"Grandpa, how did you folks do to poop without having a smartphone?"
"We used this great thing called the Penrose ceramic tiling. We never had the same poop in our entire life."
when i watched this video a year ago, i wondered why the aspect ratio is slightly less wide than the standard 16:9. the answer just clicked in my brain: it's the golden ratio. very nicely done
This video is especially inspiring! I really appreciate your work!
11:49 "It's futile"
No, it's many tiles.
I hate that I broke out laughing to this
Gah you beat me to it. Although I was going to go with "fu-tile".
How 'bout 'few-tile'?
💀💀💀
Fulltile.
“The time you waste will accumulate over your life time” I didn't need that personal attack today, thanks Derek
.
udaynath290493 i actually read this heen he said this
"you might look further out, but it's fu*tile*" :P
@@Koningg_ ME TOO! :D
Someone did it! Found one shape that when put together never repeats!!
In 2012 I attended a talk by the very Dan Schechtman about quasi-cristals. His talk paled in comparison to this video. I walked out of there with absolutely no idea of what quasi-cristals were, but you made it cristal clear to me (pun not inended) in just 20 minutes. Goes to show you the, not just importance, but NECESSITY of science communicators to spread knowledge.
When I saw the golden ratio and fibonacci sequence, I was like
"Oh yeah, it's all coming together"
But in reality,
I still don't understand a thing.
This guy gets it
I came here to comment something similar. But you said it best :D
You said the exact thing what everyone felt while watching this video but could not gather guts to accept.
12:55 While "five-fold symmetry" can definitely be connected to the golden ratio through the square root of 5, aren't the "0.5" elements in his framing of phi just an accident of base-10 expression? For example, in base-6, the expression would be "0.3 + (5^0.3)*0.3"
If you really want to go down a rabbit hole check out "quantum gravity research" on youtube they are trying to make use of higher dimensional quasi crystals to experiment with theoretical physics in some kind of simulation. Theres alot l of videos now though i started watching when they started.
Students: Learning shapes is for kids!
Shapes: *•-•*
I don't understand why you couldn't have written this out as a sentence instead of a exhausted meme format that is renowned for being a like farm.
Vorshack uhh... what?
Lol
Vorshack wtf
Vorshack ar u oke
We are so happy that you enjoyed Prague!!
It's a stunning combination of being mind-blowing, counterintuitive, and breathtakingly beautiful.
Isn't it weird how this could be a lecture in some school and we'd all be falling asleep, but this guy managed to make it so interesting that 3m people decided to watch it?
school forces you to learn, this video is optional and encourages curiosity.
Ghost Anon your comment makes no sense
yeah why are we all here rn 😭
@@inzaghi8935 Unfortunately, that says more about you.
Ghost Anon the fact that he’s not paying attention already disproves what you’re saying
Class today we'll be learning about shapes
Class: LOL shapes are for kids
Shapes:
😂
Imagine saying shapes are for kids, I be you are a kid, wait till you have to draw that shapes and joke isn't good.
TT12- Roblox and more Our most sincere apologies, grandfather!
TT12- Roblox and more | Imagine saying shapes are for kids. I bet you are a kid, wait ‘till you draw those shapes. Your joke isn’t good.*
TT12- Roblox and more It’s ironic how you are aware it’s a joke. It makes me utterly indecisive whether to laugh or be annoyed.
Really well illustrated... worthwhile subscription
truly amazing, the mysteries of geometric nature
some parts of this video blew my mind away
Is anyone else here seriously excited to learn this stuff like I don't think I've ever been so thrilled by a math lecture
Na
euridite
School wants kids dumb
Presentation is everything
Same! Seeing the 'rules' of science being broken down and applied in new, strange ways is seriously cool.
My small ass brain just pretending to know what he's saying: *mm yes ah yes mhm yes indeed quite correct*
That’s me lmao 🤣🥲😭
can relate
lmaooo same
Lol same
Mm, yes, dodecahedron... 🤔🤔
The fact that there are uncountably many tilings of a penrose pattern is mind blowing. I would love to read the proof of that, and hopefully one day understand it.
My Physics 581 (solid state physics) teacher briefly metioned quasicrystals in class today and I remembered this video. I went back and watched it again with a new perspective and it totally blew my mind. I'v always loved Kepler's wierd geometric obsessions, so this was cool to see applied to my field of study!
Nerd
One of the most interesting classes I ever had
Bruh
Is this a normal coment???
@@stefanleu4278 er yeah
@@AFKBIN lol
@@AFKBIN oh hi there
Definition of a pattern: "It must repeat"
Penrose Tiling: "Hold my rhombus"
😂
team sucks lol
Dont care didn’t ask
Lol 😂
To be precise: things that repeat are called "periodic". They exhibit "periodicity". The Penrose tiling exhibits what's called "quasi-periodicity"; it's "quasi-periodic".
I gotta stop watching these but they are so good I can't!
Your bit about infinity, how there are an infinite number of patterns made me think of the multiverse theory. Some people focus on how in the multiverse there could be wildly different things than we're used to, but there could also be an almost identical replica, so infinitely near perfect that it'd be impossible to ever know the difference.
I love how Veritasium has transitioned from physics into geometry, chaos theory and more math topics. Would love to see him cover some of graph theory as well!
Yes bro
Vsauce and Veritasium . the two gems
but what are gems????????????
What he really needs to cover is social justice and how white supremacy causes people to believe this "science" is true.
@@LouSaydus are you suggesting that non-white people are unable to think with the sophistication presented here? If yes, you are racist.
I mean, these are all things that were briefly discussed in my physics BA, but yeah they're mostly math-y
Moire pattern: exists
RUclips quality: adios
Compression algorithm: *sweats profusely*
Xeno Kudatarkar
Video compression works by simplifying RGB and chroma data in patterns. The fewer patterns(repetition), the less effective the algorithm. Then you get a blurry or blocky picture. :)
Maths : QUESTION
Factor high degree polynomial
ruclips.net/video/D99PASilPrY/видео.html
See one time
@@timothymiddleton6651 I think you can force it is to use less compression, not sure about h264.
Your obsessiveness is an inspirational. Thank you
One of the best videos out there
The madlad actually made this video's aspect ratio the golden ratio :D I was so confused until I divided the pixels after watching the video. Nice touch 👍
Same here
No really?
I can confirm, nice catch :D
Yeah... same 🤥
@@Luke-zw5el yep :D 1748/1080=1,61852 (close enough)
Me: this video is very neatly presented
My brain: h e x a g o n s a r e t h e b e s t a g o n s
Lol I keep thinking that too
I've just seen it lol
am i the only one who noticed a CGP Grey reference in this comment
@@pyrthero ok good
@@Zhuk-zc8es that's literally the whole joke
They actually found one shape that doesn't repeat.
This one of the best RUclips videos ever made.
My parents thought about renovating the upstairs bathroom, I think I just found the perfect floor tiles!
This video will start a trend, for sure.
imagine the poor guys having to set those tiles :))))
Perfect for when your bathroom is infinitely large and you hate reptition
yep.. i thought.. " that's our patio sorted " at one point
You guys have an upstairs bathroom 🙃
11:49 "It's futile."
No man, it's very many tile.
humorous joke my good man
Dad?
It's infinitile?
It's Tilenol.
This is just wild. I have no idea what I just watched but it was still amazing and gives me a bigger respect for the universe around me
Time to make an update!
As a physics and mathematics major I can’t find any video of Derek’s that isn’t totally enthralling. Let’s all take a moment to congratulate Penrose for his prize and Derek for such consistency and quality in all of his videos. You truly make the world a better place!
I haven’t enjoyed a video of his for years
@@westernbrumby why so?
@@westernbrumby lol
“As a physics and mathematics major”
Fun fact: Keskuskatu in Helsinki, Finland is tiled with this pattern, and I’ve always felt pretty uneasy about the fact that it doesn’t seem to repeat. Now I know it doesn’t.
I looked it up, it's a square (ironically named now, should be pentagon to retain some of the symmetry, but I can't find an aerial image) tiled with a penrose tiling. Not many good pictures of it, math isn't all that interesting to tourists if it is beyond the price of coffee.
I thought this pattern looked familiar, that's pretty cool
I allways thought it did repeat on some level but now i know it doesn’t
Thanks for this! I hadn't noticed it before, but I gotta go there and see it for myself the next time I go to the capital.
The pattern doesn't repeat but it does contain the Fibonacci sequence which means there is an ORDER that is special.
Loved the Moire play with the transparencies! I think I may have to get some printed up!
You are one of or even THE best science channel
All I need is some tiles on my kitchen wall with a non repeating pattern
Now you know how.. You'll just have to decide your 2 base shapes.
Oh god ,imagine it in a restaurant. People would go insane seeking for a pattern. You know when you're bored at a dinner and you seek patterns on wall tiles?
@@eval_is_evil I would be not insane, but amazed, - tile that so perfectly fits, but never repeats... actually, before this video I thought this is impossible
I've spent time looking for the pattern in the wall of a campsite bathroom (I did manage to find one), I don't want to think how long I would be looking for one in a restaurant.
😂😂😂😂
imagine if keppler was resurrected, he must be so frustrated that he almost figure it out
No, he'd be very proud because he was in the right path
Love the profile picture
@Scom Tott nah nah, it's: Jowaness Keiper. Because why not?
I think he would be proud. Because he WAS right!
@@ryangraham6878 Still is right.
12:36 THE GOLDEN RATIO STRIKES AGAIN! Ever since I learned about the golden ratio, it just inexplicably shows up everywhere. It's truly amazing how so much of our reality is connected by this simple ratio.
Mind blowing and very exciting!
Saving this to my “don’t watch while you’re high” playlist
Saving this to my “watch while you’re high” playlist
Thank you for the idea of that playlist
@@1TieDye1 I concur 😁
Even watching this one sober put me in that state a bit ✨
I love that you actually made a playlist just for this vid, Yes, i checked haha
Too late. I just learned a lot about the fabric of spacetime.
Haha, 420 likes :D
IT'S THAT DAMNED GOLDEN RATIO AGAIN! IT'S INESCAPABLE!
MATH IS A JOJO REFERENCE.
Must be some geometric magic
The only non jojo reference in the world is... OTHER ANIMES
@@St3lla-MaR1s exactly
@@field5758 The magic of 5-fold symmetry.
Absolutely brilliant!
Update the video, new aperiodic tile just dropped
My mind was blown several times through the course of this video, well done.
Maths : QUESTION
Factor high degree polynomial
ruclips.net/video/D99PASilPrY/видео.html
See one time
true
@@mr.knight8967 IT'S FU-TILE 11:48
What are the odds, that you think and found other thinking same, well in general close to zero but sometimes videos like these probability is very high, after watching video I thought I would write - " blown 🤯 " but found this comment which is from a person whom I know, I think I know you
Go ahead and try the Banach-Tarski paradox over on Vsauce.
someone should start a home renovation company called Penrose Tiling Company. specialize in bathroom tiling, tile flooring, and roofing or something
lol the same idea occured to me, too: I just added a new note to my 'interior design tips' spreadsheet to create a Penrose-type tiling where possible : ))
@UCB7yFRL1a7G4b18-GynCNJg hehe, nice. Thanks for the heads up! ;)
"Penrose Tiling. Making people high without drugs!"
@@mihan2d LMFAO
there is areason there isnt one, it wouldnt work
There is now a 1 tile version
This is fascinating! Oh and I lived and still live in Prague my whole life
I came here to look for a cool tiling pattern for my kitchen
I have now left with a degree for geometry
i think i just proved my teacher wrong and now teach geometry to the french
Aarav swamy what
@@nekomimitheiii6091 bro?
How big is your kitchen?
Lmao
After watching this
*Me looking at my carpet patterns*
hmmm...periodically
😂😂😂
*looks down at throw rug*
"this looks like a Nascar race track....."
*breaks out the hotwheels*
doubleutubefan5 awesome
This man's enthusiasm, individuality, and presentation is quite the treat. These are the types of teachers kids need to stay focused and excited.
Imagine proving your teachers prideful theory wrong.
I’d just be like “only A’s and I won’t tell the press”
We can't have half-an A, press.
I don't think mathematicians are the type to be ashamed of being wrong. If I were the teacher and you just said that, I would tell the press
Teachers are wrong 90+% of the time if they have to follow the scientific method.
Are you talking about Wang?
Maybe you should learn the difference between conjecture and theory. No one would (or at least should) be upset that their conjecture was proven false.
Why do we watch
11:49 "it's few-tile"
Well played
If only I were this clever
@@veritasium Hi!
Einstein tile has been discovered that allows aperiodic tiling with just 1 shape.
Any videos with link? Very curious
Time for an update...both for the Einstein tile, and for the LastPass sponsor. lolol
If a floor was tiled with this anti-pattern, I think it would drive me slowly to madness looking for a pattern
i mean, there is a pattern, it's just an infinite hierarchy
we did this in london,it was all one colour wooden,like a paraquet floor, my landlord cut out the above shape and put us to work he paid us in good nutritious food and a laid back attitude to our scrappy cleaning ect
im te kind of person to actually find the pattern
I can kinda see matching points, almost like symmetry
@@potassium6677 if you somehow found a pattern it would mean you had a mental disability which causes you to see things that aren't real / change what you see to look like something else
if it doesnt repeat does it even classify as a "pattern" anymore?
you ruined everything, stop you have much power
It does because it follows certain rules
You might be right, might just be like a lattice or maybe just a grid? Don't know
Sometimes the fact that nothing makes a pattern is a pattern in itself
@@santiago_moralesduarte tell me, what are the rules
Amazing content. Please also make a video on the golden ratio 😅
i used to play with those penrose tiles with the arcs! it's actually really satisfying to know now that the pattern Can't repeat as expected lol
Whoa, the animations at 7:30 really helped me understand Penrose tiling better than anything I've seen before :O
well hello carykh nice to see u here
Cary Kite-piece Hobbyist
Hey Cary! You should also check out jan Misali's video on the topic of all the regular polyhedra, including the Kepler-Poinsot solids, if you haven't already. He's in incredibly talented content creator that also does conlangs.
Yo hi cary
Hey Cary!
Me: just one more video
3am: G E O M E T R Y
Reading this at 3am where I am 😂
@@rgw4393 same
s h a p e
@@xxx_robloxmasteroof5160 YES
DASH
i watched it three times over one year, still amazing and it get richer..
I return to this video after knowing about the new Einstein Tile
9:15 "As i rotate around, you can see"
RUclips's compression algorithm: No I don't think they will
Godly comment right here lol
i can see it
Stuff like this is what blows my mind. Being at the mercy of mathematics, being able to prove things logically and yet never being able to verify it by observation, how a few simple rules can produce such complex behavior, etc. We really are lucky to be able to explore such things!
Math is awsome and beautiful and everybody likes it!
Haters gonna hate.
deus vult I can’t stand math, but I will admit if you’re good enough at it you can do anything given the tools
Absolutely loved this video!! but it is very near 4/1/2023, but not quite yet, where is our video on the 13 sided "Einstein Tile" my friend?????!?!?!!!!!!!
"His student...found a set of 20426 tiles that could tile the plane, but only non-periodically." Jesus, now that's a guy who had some time on his hands.
For people who love geometry, this is just absolutely inspiring.
It is. I was thinking during this video how two penrose pattern slightly rotated and scaled would make an interesting level generator if only there was a formula in stead of a puzzle.
Nah man, I keep dying in geometry.😤
For people who hate* (me)
THEORIA OMNIA est un chercheur indépendant qui a développé une théorie qui va beaucoup plus loin que ce qui est montré ici... Faites une recherche...
Geometry is for little kids