How a Hobbyist Created An Infinite Pattern That Never Repeats

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Has the Einstein Problem finally been solved? For decades, mathematicians, logicians and professional puzzlers have tried to find the existence of a single tile that by itself scales to infinity without ever repeating it's pattern. Was 2023 the year this illusive shape was found...
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Chapters:
0:00 Can A Single Shape Infinitely Tile?
0:52 Regular Tessellating Polygons
3:45 Introducing Irregular Shapes To The Problem
4:23 Non-Periodic and Aperiodic Tiling
5:56 Wang Tiles
7:16 Penrose Tiles
8:35 David Smith and the Aperiodic Monotile, The Hat
10:45 The 'Impossible' Shape - The Spectre
11:59 5 Fold Symmetry In The Real World. Dan Shechtman & Quasicrystals
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Опубликовано:

18 май 2024

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Комментарии : 230

@DrBenMiles 4 месяца назад

Want a dino tile? 🦖 Drop me a comment below! I'll announce the winners at the end of next weeks video Errata: - A clip of a spinning heptagon from a cut scene made it in, in place of a spinning hexagon - I will be forever embarrassed of this mistake - sorry.

@danielm.1441 4 месяца назад

Dinos please!

@deandavies1462 4 месяца назад

Dino please

@WeaselTM 4 месяца назад

Dino, please! 🦖🦕

@bgbthabun627 4 месяца назад

dino please!!!

@Therealpicodogg 4 месяца назад

Sounds like strange matter.

@Chaisz3r0 4 месяца назад

2:02 Ah yes, the famous six-sided pentagon ;) 3:08 and the famous seven-sided hexagon, too.

@smartereveryday 4 месяца назад

Fun video, thanks for making it.

@DrBenMiles 4 месяца назад

Thanks Destin! 🙏

@mrdarklight 4 месяца назад

Just wanted to point out, as a graphic artist and Civilization 6 fanatic, the shape you used when talking about a shape with six sides (at 3:10), in fact, had seven sides.

@jamestreydte9934 4 месяца назад

Was gonna comment this, glad somebody else noticed too😂

@DrBenMiles 4 месяца назад

Ahhh, nightmare! Thanks for the catch

@Not_mera 4 месяца назад

Same thing at 2:02, the Pentagon is a hexagon (at least the hexagon is a hexagon tho)

@ArmyGuyClaude 4 месяца назад

I’m just glad, as a physics hobbyist, that a hobbyist was able to make waves

@scootndute579 4 месяца назад

For real, the scientist gets a nobel prize for a semi repeating problem but a hobbyist figures it out and is called ... A hobbyist

@KaiHenningsen 4 месяца назад

@@scootndute579 Well, in astronomy, they're called "amateurs", and they're well known for occasionally figuring things out. Lots of astronomy stuff was first observed by amateurs. Maybe not so surprising when you consider that modern amateur telescopes are usually better than what Galileo used, plus there's photography now ... and how many objects are flying around even just in our own solar system.

@CensoredByYouTube. 4 месяца назад

The sad story of Pauling's denigration of Shechtman and his work simply reinforces for me how supremely arrogant and cliquish the scientific community can be, and how easily one can be cast out of it, lose their funding, and the resulting ability to pay their mortgages, car installments, and their childrens' college tuition, if they don't tow the party line.

@badgerchillsky535 3 месяца назад

There’s a quote, don’t remember the exact quote or who it’s contributed to, but it says that half of what we know about science is wrong, we just don’t know which half. I have a hard time taking anyone seriously who says “that’s not possible”. History is filled with examples of how humanity was certain about how the world and universe works, but later we found out it was flawed, or even completely wrong.

@CensoredByYouTube. 3 месяца назад

@@badgerchillsky535 Along those lines, speaking of quotes, one of my favorites is _"The moment a scientist declares 'the science is settled,' he ceases to be a scientist, and becomes an evangelist."_

@Jackpkmn 3 месяца назад

@@badgerchillsky535 The worst offender to me is by far medical science. Medical science study is overwhelmingly done exclusively on white men and then its just assumed that any findings can be translated and adjusted for women and people of other races.

@escthedark3709 3 месяца назад

You mean race isn't skin deep and that biological sex isn't irrelevant? Sounds like someone needs more diversity and inclusion reeducation.

@kiddhkane 3 месяца назад

Thats because white men are the ones who end up paying for 99% if meds.

@aDifferentJT 4 месяца назад

You’re somewhat incorrect in your statement of the problem, there are lots of shapes that can tile aperiodically, the problem was to find a shape that can tile aperiodically but cannot tile periodically.

@brostein6 4 месяца назад

The definition given of aperiodic was no periodic. So, given base level reasoning any aperiodic shape will be not periodic. Any periodic shape will not be aperiodic. So, I'm not so sure you're correct in your statement at all.

@IPWCsInTheory 3 месяца назад

At 0:48 he briefly shows an aperiodic tiling with a tile that CAN be tiled periodically. The previous comment is correct.

@aDifferentJT 3 месяца назад

@@brostein6when was that definition given?

@brostein6 3 месяца назад

@aDifferentJT in the video. Also a base understanding of how prefixes work.

@brostein6 3 месяца назад

@IPWCsInTheory that would make the tiling periodic.

@Autoskip 4 месяца назад

Dinos please! …though if you'd asked me what my favourite aperiodic tiling was, before the Hat discovery, it was Penrose's kites and darts, then the Hats and Spectres took pole positions when they were discovered, and then, a couple of weeks ago, I found out about the Trilobite and Crab tiling, and I quickly fell in love with its simplicity in construction, and how close it dances with looking like it should tile the plane.

@simpsonyellow 4 месяца назад

Shout out to the heptagon stepping in as the hexagon's understudy at 3:07. Pulled off a convincing performance!

@DrBenMiles 4 месяца назад

😅 I'm crushingly embarrassed that slipped through

@joe-skeen 3 месяца назад

My four year old identified a shape (incorrectly) as a heptagon the other day. I was just shocked he knew that word.

@cowgirljane3316 4 месяца назад

As a dyslexic, math has always been a massive struggle, and I had no idea what you were saying, but I am still fascinated by math and especially quantum physics. As an artist, I see shapes in everything, and that dinosaur is cool. Who says they went extinct, they are in math.

@KaiHenningsen 4 месяца назад

Many species of dinosaurs went extinct, but there are still dinosaurs around. We call them "birds". You might say that they have ... _changed shape._

@troywhite6039 4 месяца назад

They are also called lizards, gators, komodo dragons, etc. They just got smaller.

@margretrosenberg420 3 месяца назад

@@troywhite6039Nope. Lizards etc. share a common ancestor with dinosaurs, but they're basically "cousins" of dinosaurs, not descendants. Birds, on the other hand, are direct descendants of the dinosaurs.

@flameofthephoenix8395 3 месяца назад

@@margretrosenberg420 Yeah, and that's a scary thought, you can't even use the "Just need to run faster than the slowest of us" trick since those darn birds just peck everywhere randomly.

@cheeky1664 4 месяца назад

Excellent, as ever! 😊😊 Thank you! 😊😊

@En_theo 4 месяца назад

That example at the end, of a scientist to afraid to publish a proof because the "scientific" community can be so harsh with people with new ideas, that tells it all. It's the main problem in science, most of people just repeat what is deemed "true" before them and are ready to stone anyone with a new idea. Just ask John Bell ...

@thenonexistinghero 3 месяца назад

That's not the main problem in science. The main problem is modern science is just how damn corrupted it is. Something like this should be criticised. A theory holding up even under scrutiny or even if it doesn't, it leading to new knowledge and insights... that's what science should be about. Sadly modern science is all about propaganda and indoctrination for large part. Doing research often requires funding and governments and major companies won't fund if they think the results work against them or if they don't deem something important enough.

@En_theo 2 месяца назад

@@thenonexistinghero True, corruption is the other big problem. But even without corruption, prejudices would block any progress if it was not for some motivated genius. But problems in Physics are more and more complicated and it requires the help of so many different fellows to prove your theory right, that it's impossible to get there if you have a "fantastic" hypothesis.

@colatf2 2 месяца назад

@@thenonexistinghero😂😂sure bud

@thenonexistinghero 2 месяца назад

@@colatf2 Good to know you're a mindless foo.

@DonaldDucksRevenge 4 месяца назад

I love both these stories! thank you for bringing them to us!

@larryscott3982 4 месяца назад

3:09 describing rotating a hexagon. But is that a 7 sided tile?

@support2587 3 месяца назад

The deserved a subscribe! All I could think of was how to incorporated this in a remodel.

@PaulPassarelli 4 месяца назад

I first heard the term quasicrystal back in Feb '87 at a presentation at the Cornell Space Sciences building. I remember it well.

@guidodebacker4205 4 месяца назад

not my usual cup of tea, but fascinating and beautiful... thanks for explaining

@radiantthought 4 месяца назад

would you be able to share the stl for the dinosaur? I'd like to print some myself to play around with.

@ZoonCrypticon 4 месяца назад

@7:55 Interesting, "...projection of a five dimensional space with fivefold symmetry onto a 2D plane..." . One should name Penrose- Tiles "Penta-Rose"-Tiles.

@BOBLAF88 4 месяца назад

Perfect information down a road less traveled. I think E8 theory and other assemblages of ideas will eventually reveal something wonderful.😃

@gregduhon5510 4 месяца назад

My brain crashed while listening to this video. Rebooting my brain now. I will keep watching this video until my brain stops rebooting. 👍

@abcde_fz 3 месяца назад

I love learning things that only 10% of my brain 'gets', hoping that the other 90% catches up eventually!!!

@saultube44 4 месяца назад

Spectrum might had reached a Fractal Shape, since Fractals are not repeating, it should follow the tendency. But nobody checks, ironically, withe the Einstein explanation of Relativity example: 1 observer standing still and another on a moving train, turns on the light, and the observer calculates the time it takes the Light to traveler man when the Light hits to the man standing; there's a gap; is this gap Fractal? Would it contribute to such Fractal and non-repeqting pattern shape? Would it mean the University and everything in it, have such feature?

@GordieGii 4 месяца назад

@3:07 you showed a heptagon while talking about a hexagon. Was that intentional?

@Robert_McGarry_Poems 4 месяца назад

He also called the hexagons heptagons earlier in the video... Maybe he just put the clips in the wrong spot... 🤔🧐

@DrBenMiles 4 месяца назад

I think I stared at shapes moving across the screen for too many hours and became blind to them. Sorry all. Thanks for catching 😂

@Italianjedi7 4 месяца назад

Wow. It amazes me how some humans are able to figure out things that would never arise from my brain. I’m literally a kitten playing with a string compared to the thinker statue eternally thinking

@ChaoticNeutralMatt 4 месяца назад

You underestimate yourself.

@margretrosenberg420 3 месяца назад

"Always remember that you are totally unique, just like everybody else." (Sorry, I know it's a quote, I just don't know who first said it.) We all excel at something; if we're very lucky we manage to figure out what before we waste our lives trying to be someone we aren't.

@andyspillum3588 4 месяца назад

Oooh! oooh! "DINOS PLEASE" As a Very amateur "hobbyist"? (I, poorly, sculpt), I find the story super compelling (and a little bit an indictment of academia), and I've since the late '70's-early '80's been Awestruck by what that man (M.C. Escher) could do with a pencil

@antonymossop3135 4 месяца назад

What a lovely story, it put a smile on my face.

@blucat4 4 месяца назад

This is new to me, very cool content. I'm amazed that such a complex piece can be tiled, forget about never repeating. Is the universe deliberately weird, or is my brain just too simple?

@user-fz3cw1ie3l 4 месяца назад

late to finding this fascinating article. if not "dinos please", then perhaps just the 'stl' so that I could have some samples made for my college class in "Geometry and the Art of Design". we explore tessellations and even Penrose law suit against Kleenex tissue company for copyright infringement - for using his tiling patterns on the quilted sheets. Hope we do not see a "repeat" with these monotiles!!

@artstsym 3 месяца назад

Fascinating video, can't help but feel there's probably cryptographic implications to this as well, though I'm not well versed enough in either field to say what they might be.

@TomTom-rh5gk 4 месяца назад

I finally understand the problem. Dr Ben is a great explainer.

@orvilleredenpiller338 2 месяца назад

My favorite drama is geometric drama. It always comes full circle.

@charliec6020 4 месяца назад

There's a box game from Germany called "Walong" full of multiple colours of the same curved piece that may have been overlooked as a solution the inventor went straight to market as a type of child's toy rather than seek academic review, but it can be combined with itself extensively (not sure about infinite)

@zorrothomas8641 4 месяца назад

Review it, you and him can study it together and get recognition

@margretrosenberg420 3 месяца назад

I just tried searching on "Walong game" and Google kept hitting on something called "Wo Long: Fallen Dynasty." Can you provide a link?

@ytseberle 4 месяца назад

"DINOS PLEASE"! (If you have any more!) It was good hearing more about the human background of this discovery.

@kaicheung5916 4 месяца назад

Dinos please! I have always loved this problem, and the solution is so incredible.

@luciddaze248 4 месяца назад

Dino please! Renovating here and this has given me ideas...

@stumccabe 4 месяца назад

Ben Miles - when you were rotating the shape (at about 3:10) you said it had 6-fold symmetry - but you were rotating a heptagon!

@christopherd.winnan8701 4 месяца назад

Is there an existing library of periodic shapes and how they have been escherized? How can I find new shapes for this process?

@maryjones5710 4 месяца назад

Ever heard of Google, one of many search engines you can ask anything.

@Junkpusher77 4 месяца назад

My desire for a Dino has crystallized sixfold

@VisibletoanyoneonYoutubes 2 месяца назад

Everything when on psychedelics Patterns envelop every surface. Not just any patterns, but symmetrical -geometrical patterns. The human brain is wonderful

@FoxDog1080 3 месяца назад

3:07 _Accidentally picks up the wrong one_

@rikschaaf 4 месяца назад

3:07 eh... Doctor, that ain't a hexagon. :D

@Side85Winder 3 месяца назад

Daniel Shechtman: I am a sole winner of a nobel prize too, cop that Linus Pauling!

@slammish. 4 месяца назад

Pauling's response was sad. Good lesson in appeals to authority I guess. Love to give my nephews some dino-spectres.

@badgerchillsky535 3 месяца назад

Dinos please! I imagine they’re all taken, but is there an STL file?

@stischer47 3 месяца назад

Ah yes, when "experts" declare that something is impossible. I would have thought that in the 21st Century we would have gotten past that, but apparently not "Mr. 2 Nobel Prize Winner". The internet is one of the reasons that non-scientists are able to provide scientific breakthroughs, if the "experts" are willing to listen.

@holorain8410 3 месяца назад

This is the kind of logic flat earthers use to justify their beliefs

@jongrover8763 2 месяца назад

I just got told that one of my ideas is impossible within the last week. Maybe I should publish.

@torbjornalmli 4 месяца назад

@ 2:02 2 hexagons? I know they are the bestagons but still...

@brianegendorf2023 4 месяца назад

I read a book about this..its fascinating stuff. They went all the way to the coldest parts of Russia to get the meteorite to prove that these patterns can happen in nature.

@markandrews7701 4 месяца назад

I would be interested in learning how you prove that such a shape can tile a plane to infinity without repeating.

@WilliamWizer 4 месяца назад

it's easy to find a image of how to draw the einstein but I have found myself unable to find how the spectre is made. it's just curiosity but, can somebody point me to a simple source that shows how to draw those curves?

@muhdkamilmohdbaki7054 4 месяца назад

Not sure what is the application of this but I guess the Spectre shape can be made into cookies with least waste as opposed to circle shaped cookies (the most common). However, humans have been making square shaped cookies for a very long time and it won't produce any waste.

@daskritterhaus5491 4 месяца назад

my admiration for mr 2 nobels just fell 4 notches.

@jimjackson4256 4 месяца назад

So how about 3 dimensional non repeating shapes?

@inomo 4 месяца назад

Why are you rotating an heptagon to demonstrate the hexagon 6-fold symmetry?

@isbestlizard 4 месяца назад

How easy is it to make custom porcelain tiles? These would be amazing for my bathroom o.o

@mattt2812 4 месяца назад

Lol, spinning a heptagon to demonstrate 6-fold symmetry. I thought I was going nuts.

@DrBenMiles 4 месяца назад

My bad. Late night editing brain let that slip through

@marikasdaughter6263 3 месяца назад

Most of the "non repeating" patterns look like they repeat infinitely to me... At least this new shape doesn't automatically appear to repeat at all like the rest do.

@abxyabxy281 3 месяца назад

I'm letting that hat shape be reflected, because I can barely tell the difference anyways.

@troywhite6039 4 месяца назад

Dinos please This reminded me of the envy free cake cutting challenge, another mathematical algorithm If I could get the dimensions of the specter tile accurate, I think it would be cool to make a driveway or garden path from a cement tile mold.

@ESw0rdsman 4 месяца назад

The sound that precedes Scientific Discovery isn’t “Eureka”, but “Huh, that’s interesting”

@orsonzedd 4 месяца назад

I see you using that heptagon when you said hexagon

@waynesworldofsci-tech 4 месяца назад

Darn, and here I thought it was a Spirograph video!

@z4zuse 4 месяца назад

3:08 heptagon masquerading as hexagon

@alexanderstohr4198 3 месяца назад

03:07 - this shape has 7 edges and 7 corners. - dont call it a hexagon. ;-)

@Kobai36 3 месяца назад

2:00 those are both hexagons

@otteroid2 4 месяца назад

dino tile please!

@Ogolero 2 месяца назад

“DINOS PLEASE”

@m3talHalide-rt2fz 4 месяца назад

price of a stock over time are the 2 dimensions we all use..

@pixelanthony 3 месяца назад

2:00 That's a hexagon, not a pentagon.

@inguszemene1098 3 месяца назад

2:00 you did 2 hexagons

@dentstroyer 2 месяца назад

3:08 thats a heptagon

@Freerangerification 4 месяца назад

"DINOS PLEASE"

@AllToDevNull Месяц назад

It is very funny and sad, when you understand that we have a unified physics theory that predicted everything correctly for 20 years now and is ridiculed or just ignored by the masses of physicists.... Stoyan Sargs BSM-SG model has predicted most phenomena that modern physics is puzzled about

@imtootired1993 2 месяца назад

But isn't the textbook definition of the word pattern "a repeated decorative design"?

@themexyeti 2 месяца назад

3:07 wasn't a hexagon

@uncleroach 4 месяца назад

I wonder how many discoveries are beeing keept in drawers due to ego of supperiors or colleauges?

@KaiHenningsen 4 месяца назад

So ... should we have defined a circle as 12 degrees (or whatever other name)? That's the one that evenly divides into 3, 4, and 6. We're just lucky that 360 is 12*30. Weight of Pauling: he also was a vitamin C cook. Rock star scientist ... Brian Cox? Brian May? Some other Brian?

@bkparque 4 месяца назад

A 2d representation of a 3d cube representing 2d logic and trinary logic

@terakhan6656 2 месяца назад

To answer the question in the opening seconds, no. By definition, a pattern repeats. If it doesn't repeat, its not a pattern.

@spiraldude 4 месяца назад

Now do it in non-Euclidean space.

@jamesjenkins8882 4 месяца назад

Anyone notice that he showed a 7 sided "hexagon"?...😅

@humanbeing-_-_- 4 месяца назад

Dinos please! If it’s not too late! Also, this is incredibly cool thank you for letting me learn something. Incredibly neat today.

@billyjhamlin 4 месяца назад

Chirality makes different shapes in proteins, why not hats?

@mineman2142 3 месяца назад

3:07 that's not a hexagon

@ebbinandflowin 4 месяца назад

Funny how you're talking about the hexagon at the 3:08 mark yet the geometric shape you're showing is the heptagon. On purpose to be sneaky or just a mere oversight?

@TBButtSmoothy 4 месяца назад

hexagon! *shows heptagon*

@margretrosenberg420 3 месяца назад

If I'm not too late, Dinos please.

@user-p4w5jnef5w6fu 23 дня назад

Dinos please!

@soundmaster1966 4 месяца назад

2:02 And where is the Pentagon? Your third figure shows 72 degree by definition? Wow. That is keen.

@saultube44 4 месяца назад

There's a reason for the saying: "Science advances from funeral to funeral"; our limited minds, can only adapt so much, to the weirdness of the Universe 😊