The Infinite Pattern That Never Repeats

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 YouTube)
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

[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”

[wuddadid]

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"

[DavidSallge]

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."

[memerminecraft]

They've recently discovered a single tile that accomplishes the same thing on its own! Would love to see this revisited.

[aarushrout]

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!

[shotatoriumi]

Me: Gives this pattern to the guy tiling my kitchen

Tile guy: Sweats profusely

[briannawarren]

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.

[irenanovakova]

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!

[liudvikassablauskas]

Just right now they found the first single tile that tiles the plane aperiodically, calling it "eistein". Amazing breakthrough! It does however require mirroring

[aspeneatherton]

“Well it’s infinite, so it’s gotta repeat at SOME point, right?”

Scientists: “lmao no”

[roowyrm]

Huge thanks for this!!! I love these 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 all because of pattern in maths. And it was all started by my fascination with Fibonnaci (amongst other mathematical patterns)

[thfelixraven]

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

[wallaceroberts]

Builder: So what kind of tiles you want in your bathroom then?

Veratasium: Well....

[katieerickson]

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

[shreeyaksajjan]

Your visualisations are stunning. Such intricate patterns, drawn so beautifully

[mason]

Ive never said this in my like, 10 years if watching youtube, but I wish I could pay you for making videos this good.

[jmir]

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 👍

[hoihoi]

"daddy, what do you do?"
"I look at shapes"
"That sounds easy"
"Well I also look at colours!"

[nicholasserrambana]

great video; I've been looking for rigorous but recreational math content like this on Youtube for years!

[jan-pi-ala-suli]

update: there’s a new aperiodic monotile, which can’t even tile periodically with its mirror image, or tile at all with it, only ever aperiodic and with its own image. it’s called the spectre, and it’s part of a family of tiles which tile with their mirror images but only aperiodically, with three exceptions at the limits of sizes of the edges. two other ones are the hat and the tortice