The Infinite Pattern That Never Repeats

72 869
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 NOburn)
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
Runtime: 21:11


Veritasium - 14 dager siden
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 - 3 dager siden
...which has nothing at all to do with this video.
Flick Penrose
Flick Penrose - 3 dager siden
Wait ... we didn't already know that? :O
KyrilPG - 4 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 : 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
Pranav Pothanis - 4 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
Pranav Pothanis - 4 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?
The Entourage
The Entourage - 5 timer siden
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.
Patrick Hoesly
Patrick Hoesly - 5 timer siden
Mind blown! I need a lie down.
Aviation Hobbies
Aviation Hobbies - 6 timer siden
He is the new vsauce
Steven Glowacki
Steven Glowacki - 7 timer siden
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.
armondtanz - 7 timer siden
Ok, what hav i got to do right now in my life to understand thsi vid?
Somewhat Blank Paper
Somewhat Blank Paper - 9 timer siden
The hardest part is actually proving the conjecture lol.
Jacob Gould
Jacob Gould - 10 timer siden
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.
Nutthatch Wood
Nutthatch Wood - 12 timer siden
I need that big d20
soinhu foitu
soinhu foitu - 9 timer siden
This is at least a hint at why re-evolution is eternal sync-duration connectivity.
Awes - 12 timer siden
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
soinhu foitu - 9 timer siden
Good job.. keep up the good work.?
çağatay tuncer
çağatay tuncer - 12 timer siden
my brain melted and I want to tile the whole house
Dan Z
Dan Z - 13 timer siden
uh huh
Fiesta_Blend458 - 13 timer siden
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
Mike O'Barr
Mike O'Barr - 14 timer siden
Well this video was definitely time consuming to produce. Thank you for making and sharing this with us!
Luxray Lloyd
Luxray Lloyd - 14 timer siden
Dam, Maths is so freakin cool!
Luxray Lloyd
Luxray Lloyd - 14 timer siden
I'm pretty sure i did something like that when I was a kid (it wasn't infinite, but I did try)
Breno Faria
Breno Faria - 15 timer siden
Why are people so confused? It's an interesting and clear message lmao
Professor Perry
Professor Perry - 15 timer siden
Congrats to Penrose on winning the Nobel Prize! Fascinating video as always. It is amazing how these patterns exist in different fields.
Ayden Sibbern
Ayden Sibbern - 15 timer siden
Who else here's a child in the background? 10:31
tabaks - 16 timer siden
1Password is leaps superior over LastPass.
DRakeTR of KBam
DRakeTR of KBam - 17 timer siden
This is the most intelligent illuminati confirmed video ive ever watched
2Tri - 17 timer siden
This is the most coincidence-filled thing I have ever seen in my life...
Релёкс84 - 17 timer siden
then you probably don't know what the word coincidence means...
Ofir Dolev
Ofir Dolev - 17 timer siden
Rrally interesting, but my guy are you really not saying that they are also dnd dice
Aleksander Sowiński
Aleksander Sowiński - 17 timer siden
David Wilkie
David Wilkie - 18 timer siden
This is at least a hint at why re-evolution is eternal sync-duration connectivity.
Lucas Vidal
Lucas Vidal - 19 timer siden
Does anybody know where i can find the patter to print the tiling and transparency used to see the morie pattern?
Neil's - 19 timer siden
Drinking game : drink when he say 'periodically' or 'tile'.
I'm bloated.
Dean Howell
Dean Howell - 19 timer siden
Rubic's club plays in here somewhere, right?
Vellweb - 19 timer siden
nah ill stick with Dashlane instead of LastPass
Laure_lei - 19 timer siden
The real mystery is how you spread these out all over your floor with multiple littles in your sphere and still maintained all the pieces. (Worm holes? Superposition? Nap time? Enquiring minds want to know.)
Ken Rossman
Ken Rossman - 19 timer siden
Wow! Show me how to do that trick where you toss a polygon up in the air, and it morphs into a different polygon! That was really cool!! :-)
Ken Rossman
Ken Rossman - 17 timer siden
@Релёкс84 that was sarcasm on my part... :-)
Релёкс84 - 17 timer siden
it's called video editing
B88 - 20 timer siden
Amazing - love it!!!!
Solo Recibo Spam
Solo Recibo Spam - 20 timer siden
18:04 Please, i would like to know more about such rules. Where can i find more info on that? Thanks.
123 M
123 M - 20 timer siden
Maybe physics is not my cup of tea😑😞
john sims
john sims - 22 timer siden
Duh ...
Hamish Forrest
Hamish Forrest - 22 timer siden
Why does it need to follow the lines?
Stibble - 23 timer siden
If math was this cool i would have paid more attention
kaczan3 - 23 timer siden
This guys travels, has an wxpensive hiuse full of toys. His life would be awsome if he didn't have that long term gf or wife or w/e.
Kono DIO da
Kono DIO da - Dag siden
This is the secret of the Zeppeli's infinitely spinning steel balls.
ps: definitely not a JoJo reference
Релёкс84 - 16 timer siden
cringe weeb
bofooit gojo
bofooit gojo - Dag siden
The question that occurred to me: is there a relationship between space-time and Penrose tiling?
Cabillo, John Benedict
do you have any friends to help you out there???
Janezjanez Novaknovak
Janezjanez Novaknovak - Dag siden
It turns out that he was Wang.
bofooit gojo
bofooit gojo - Dag siden
What are your thoughts on the possibilities of encoding information within a quasicrystal structure? With the infinite possibilities of arrangement, it seems this should be
Javier Borda
Javier Borda - Dag siden
Washington DC
Tommaso Gambassi
Tommaso Gambassi - Dag siden
te stai male
Memed Tracks
Memed Tracks - Dag siden
Bruh you did this for nothing, Military camo is also considered a pattern and yet never repeats since a repeating pattern in it would cause people to see it quicker.
Antonio Garcia
Antonio Garcia - Dag siden
absolutely crazy that the tiles of the 2 tiles non-periodic shape matched up with what Kepler's drawing of a non-periodic shape. It's actually really profound to me that it matched up, it really puts us and our minds into perspective for me.
Tony Veretyuk
Tony Veretyuk - Dag siden
Hi, there! I am amazed by your wonderful video! I am a professional translator and I would like to translate this particular video into Russian. It all sent shivers down my spine how 1 question leads to another... and another... and another... infinite :) Please contact me:
Josh Bowman
Josh Bowman - Dag siden
And yet even more evidence that there is an intelligent creator behind our beautiful universe. Don't hate me for saying it just look into the evidence! If you want Scientific answers, any of Josh McDowell's five books called The New Answers are great for that. If you want logic based research, my suggestion is The Case for Christ by Lee Strobel.
Dawsieboy Gaming
Dawsieboy Gaming - Dag siden
At 2:13 please stop using the scp illustrated music it’s throwing my brain off
Lach Vogel
Lach Vogel - Dag siden
At 4:44 when rotating Keplars 5-way symmetry tiling, the centre point should be the star below your axis point instead of the decagon.. But yeah, how does one continue the tiling.. ;) Great video otherwise!
Zane Gant
Zane Gant - Dag siden
I don't know how many times this video blew my mind.
Cédric S
Cédric S - Dag siden
That's even tougher than watching Tenet..
fluke9 - Dag siden
wow! thanks
Sub because Why not
Sub because Why not - Dag siden
1.58 I swear that is the music for a game and what is it called
Dean Ashworth
Dean Ashworth - Dag siden
Imagine this intelligent and without all the technology of today....f@!k me the astronomy stuff blows my mind
douglas mccann
douglas mccann - Dag siden
22 over 7
Haytham Abdel-Qader
Haytham Abdel-Qader - Dag siden
half-life 3 confirmed
Rather B. Squidding
Rather B. Squidding - Dag siden
What are your thoughts on the possibilities of encoding information within a quasicrystal structure? With the infinite possibilities of arrangement, it seems this should be possible assuming you can control exactly how the quasicrystal grows. If this is possible.. it makes the extraterrestrial origin of the only quasicrystal ever found very interesting. Could it be a message from a far off alien species? I think so. Shameless plug: More information in this video:
Liam Revorêdo Pinto
Liam Revorêdo Pinto - Dag siden
Is this like turning an irracional number into something physical?
TheManWithManyNames - Dag siden
I just wanted to know a good tile pattern for the floor. I wasn't expecting a scientific lesson.
Trainer JB
Trainer JB - Dag siden
The pictures of the two crystals that had electrons scattered off of them almost looks like the cross-section of a myofibril
Meagan Brady
Meagan Brady - Dag siden
Sam Al-Sapti
Sam Al-Sapti - Dag siden
Anyone else noticing the confused lady at 0:31?
YOUR ANIME HERO! - Dag siden
this is just us looking at dimensions we cant see.
YOUR ANIME HERO! - Dag siden
use this for mapping space
Evanduril - Dag siden
I was lost in the begining, but man, that was exciting to watch.
boya hawken
boya hawken - Dag siden
anyone here from science class👀
Graham McMullen
Graham McMullen - Dag siden
Thank you for this great mental distraction. Putting my cat down today has had me feeling pretty terrible, but I was able to escape that for a moment while watching this.
no one expected the spanish inquisition
Make these patterns in glass, shine light through them, you need quite a few layers, you will find that the geometry of the light will change... It will gain mass.. exotic mass.. Use electromagnetic fields to control the mass that happens to flow through in just the right way.
bhishma pitamah
bhishma pitamah - Dag siden
*me not understanding anything and coming into comments*
me after seeing comments: ah, I'm not the only one.
Mathew Silva
Mathew Silva - Dag siden
Got It So We Have A d6,d4,d8,d12 and a d20
Jérôme TOUATI - Dag siden
Great research work!
Binge Squad
Binge Squad - Dag siden
And this is the solution to the COD Mobile Puzzle
Mr.Spoon025 - 2 dager siden
How do you do this good of educational stuff?
minij hooi
minij hooi - Dag siden
useless skill
Anuj Bhandare
Anuj Bhandare - 2 dager siden
What if this is how the atoms of the 2nd dimension work.
minij hooi
minij hooi - Dag siden
That was brilliant.. thank you!!!?
N m N
N m N - 2 dager siden
OK this time he has succeeded to hurt my eyes and brain at the same time
Killer Queen
Killer Queen - 2 dager siden
11:50 kore ga requiem da! after 5 seconds
rrawwbb - 2 dager siden
Magnum Dong Adventures
Magnum Dong Adventures - 2 dager siden
Man penrose is 89 and still kickin!
Theironsword - 2 dager siden
The problem with a pattern that never repeats is that a pattern is, by definition, supposed to repeat.
Релёкс84 - 17 timer siden
1101001000100001000001... this is a pattern that never repeats. A pattern absolutely does not have to repeat.
Laure_lei - 19 timer siden
I have sewing patterns with no repeats, and when I open my phone's lock screen, I trace a pattern to do so. Only repeating patterns repeat.
Nathan Taylor
Nathan Taylor - 2 dager siden
Question - What is the significance of the colour variations in the tilings shown (around 04:00)?
The rhombus pattern as shown has three colours, then equi triangle and square has only 2, then hex has 4??
Is this just arbitrary in the video presentation, or is there a reason or significance for these differences?
The first hex pattern showed one colour only. In the last "six-fold, spinning" presentation, there are four different coloured hexagons, and if you rotate 60* (for example), sides align but colours do not.
jman t
jman t - 2 dager siden
i love this because... how could you not, but i hate it because now i feel like a total idiot
TheBlueGuy - 2 dager siden
I'm sorry to say this, but your title is redundant.
redbeam_ - Dag siden
did you watch the video?
Rem Lezar
Rem Lezar - 2 dager siden
"there are no quasicrystals, just quasi-scientists" sounds like someone who's jealous they didn't figure it out first and or don't like actual science.
rzeka - 12 timer siden
Thanks rem lezar I always believed in you
yes no
yes no - 2 dager siden
yknow, the easiest infinite pattern that never repeats is just counting by 1
Tom Norton-Platford
Tom Norton-Platford - 2 dager siden
9:00 how can I get these sheets?
None of your Business
None of your Business - 2 dager siden
So your _definition_ of "repeating" explicitly excludes *rotation.*
I'll say that's oddly specific...
-Nameless- - 2 dager siden
Now i want to make a floor of those shapes.
Kristie Hansen
Kristie Hansen - 2 dager siden
Prague is that where the giant books were found? How does the fractals fit in to this story? Oh I should have just waited for the answer.
Fawna - 2 dager siden
useless skill
David Wahlstedt
David Wahlstedt - 2 dager siden
Great video - thanks! Aperiodic tiles existed already in the 1400's in Iran, according to Peter Lu. See this:
Multex - 2 dager siden
im brain fucked
Nikolai Westall
Nikolai Westall - 2 dager siden
This was fun thank you!
orfo70 - 2 dager siden
mind blowen 🤯
Flaming Karma
Flaming Karma - 2 dager siden
this makes me miss vsauce.. it sounds like something he'd make a video on
Luuk Stehouwer
Luuk Stehouwer - 2 dager siden
Awesome video!
One small remark: you are really only talking about rotational symmetry. For example, I would say "a square lattice has four-fold rotational symmetry". Namely, a square lattice also has reflection symmetries next to its translation and rotational symmetry. Keeping these in mind is important if one talks about general wallpaper groups.
Josh Colley
Josh Colley - 2 dager siden
Does anyone else want to make a floor tiling with these???
samnan kadri
samnan kadri - 2 dager siden
Thank You for delivering such a great piece of knowledge....your videos are interesting always
karma tsering
karma tsering - 2 dager siden
this is the way to generate random numbers that is good for encryption which is used in network and communications
Cassie - 2 dager siden
The question that occurred to me: is there a relationship between space-time and Penrose tiling?
Bryan Valencia
Bryan Valencia - 2 dager siden
Nosebleed pero ansaya hahahahha