Why Penrose Tiles Never Repeat

Sdílet
Vložit
  • čas přidán 30. 11. 2022
  • The first 200 people to brilliant.org/minutephysics get 20% off an annual premium subscription to Brilliant. Thanks to Brilliant for their support.
    This video is about a better way to understand Penrose tilings (the famous tilings invented by Roger Penrose that never repeat themselves but still have some kind of order/pattern).
    This project was a collaboration with Aatish Bhatia (aatishb.com).
    REFERENCES
    Explore Penrose and Penrose-like patterns: aatishb.com/patterncollider
    Video by Derek Muller/Veritasium about Penrose Patterns: • The Infinite Pattern T...
    Music algorithmically generated, algorithm designed by Henry Reich
    N.G. de Bruijn’s paper introducing the pentagrid/Penrose idea: www.math.brown.edu/reschwar/M...
    De Bruijn, N.G., 1981. Algebraic theory of Penrose’s non-periodic tilings of the plane. Kon. Nederl. Akad. Wetensch. Proc. Ser. A, 43(84), pp.1-7.
    Here are some excellent in-depth references on how to construct Penrose Tiles Using the Pentagrid Method:
    Penrose Tilings Tied up in Ribbons by David Austin: www.ams.org/publicoutreach/fea...
    The Empire Problem in Penrose Tilings by Laura Effinger-Dean: www.cs.williams.edu/~bailey/06...
    Pentagrids and Penrose Tilings by Stacy Mowry & Shriya Shukla: web.williams.edu/Mathematics/...
    Penrose Tiling by Andrejs Treibergs: www.math.utah.edu/~treiberg/Pe...
    Algebraic Theory of Penrose's Non-Periodic Tilings of the Plane by N. G. de Bruijn: www.math.brown.edu/reschwar/M...
    Particularly good and helpful, and (we think) an undergrad thesis which is impressive!: www.cs.williams.edu/~bailey/06...
    An interesting popular science read on the discovery on quasicrystals and their connection to Penrose Tilings:
    The Second Kind of Impossible by Paul Steinhardt: bookshop.org/books/the-second...
    Support MinutePhysics on Patreon! / minutephysics
    Link to Patreon Supporters: www.minutephysics.com/supporters/
    MinutePhysics is on twitter - @minutephysics
    And facebook - / minutephysics
    Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute!
    Created by Henry Reich
  • Věda a technologie

Komentáře • 875

  • @carykh
    @carykh Před rokem +1698

    4:25 Wow, the proof of why it never repeats is pretty elegant! It also makes sense why a "tri-grid" (triangular tiling) DOES repeat, because sin(120)/sin(60) = sqrt(3)/2/sqrt(3)/2 = 1/1 = 1, which is rational. That explains why, when you take a ribbon of a triangular tiling, you see the same number of upside-down triangles and rightside-up triangles: it's a 1:1 ratio.

    • @ikbintom
      @ikbintom Před rokem +64

      Maybe on a curved surface, the ratio can be changed to become rational and a pentagonal tiling does repeat

    • @WildEngineering
      @WildEngineering Před rokem +11

      woah nice catch cary :)

    • @NatLJ
      @NatLJ Před rokem +2

      That’s pretty interesting!

    • @chiken-nugies
      @chiken-nugies Před rokem +14

      @TimesByTwo you just did that

    • @Pearll_.
      @Pearll_. Před rokem +4

      Oh hey cary

  • @McLoelz
    @McLoelz Před rokem +160

    I saw a bus seat pattern just a couple of weeks ago and it drove me nuts that the pattern seemed like it should repeat but every time I thought I figured it out there were one or two elements that were off.
    Thank you for reassuring me that I'm not crazy! And educating me in an entertaining way at the Same time.

    • @mctooch
      @mctooch Před rokem +5

      I saw that pattern in the back of bus seats too. Just awful the things some kids carve in there!

  • @thefreshest2379
    @thefreshest2379 Před rokem +270

    The golden ratio shows up in nature a lot because it is the main part of an efficient packing algorithm. Thanks Numberphiles!

    • @noshiko5398
      @noshiko5398 Před rokem +8

      do you remember which numberphile video that was? i just checked and they have a bunch of videos on the golden ratio

    • @maxthomas-bland4842
      @maxthomas-bland4842 Před rokem +31

      @@noshiko5398 the 'most irrational' number

    • @noshiko5398
      @noshiko5398 Před rokem +4

      @@maxthomas-bland4842 thank you!!!

  • @onatic6346
    @onatic6346 Před rokem +2431

    you know it’s a good day when minutephysics drops some obscure math problems

  • @TesserId
    @TesserId Před rokem +645

    I notice that they're said to be _quasiperiodic_ and not nonperiodic. This is the thought that came to mind when you started laying out the _parallel ribbons,_ because they definitely have at least some periodic nature.

    • @lonestarr1490
      @lonestarr1490 Před rokem +52

      It's actually not so easy to put the difference between _quasi-periodic_ and _not at all periodic_ in rigid terms.

    • @npip99
      @npip99 Před rokem +67

      It's quasiperiodic because a given particular sequence of tiles along a ribbon does repeat over and over again. However, its repetitions occur at irregular intervals, and is overall still non-periodic as well.
      It's a bit different than a sequence of integers in which there is no repetition at all, that wouldn't have the feature of quasiperiodic.

    • @cheshire1
      @cheshire1 Před rokem +12

      @@npip99 if you keep generating random integers you will find every finite sequence infinitely often, so your definition would make random numbers quasiperiodic.

    • @lonestarr1490
      @lonestarr1490 Před rokem +18

      @Artem Down He didn't said that the sequence of integers is random. Could simply be a strictly increasing sequence of integers; then you definitely have no repetition.

    • @kazedcat
      @kazedcat Před rokem +15

      That is the difference. Quasiperiodic will not give you all possible sequence. Some sequences are guaranteed not to appear in quasi periodic sequence. Like primes. Primes are not random it is guaranteed that no primes will be divisible by 6 or 10 or 15.

  • @davidtitanium22
    @davidtitanium22 Před rokem +279

    Finally i understand why it never repeats, veritasium made an interesting showcase but i never understood why it never repeats

    • @iwanttwoscoops
      @iwanttwoscoops Před rokem +28

      I still don't get why it doesn't repeat. Could someone help?
      edit: oh my God lol, I thought the video ended at 3:15 when he mentioned the friend's website. Too used to clicking away from sponsors :p

    • @msclrhd
      @msclrhd Před rokem +7

      @@iwanttwoscoops I don't have an exact proof, but know the general gist of how it works. With the square and triangular grids, notice how all the intersections of lines all meet at a point, and that the spokes radiating out of that point are all regular and form a neat tiling pattern. Then compare that with the pentagrid, where only some lines meet each other, and you get groups of "near misses" where several lines almost (but not quite) meet. -- It's that almost but not quite meeting that makes the pattern non-repeating.
      The number of spokes S is 2 times the number of parallel line sets L, so S=4 for square (L=2) grids, S=6 for triangualar (L=3) grids, and S=10 for penta (L=5) grids. The angle between two closest parallel line sets is 360/S (90 for square, 60 for triangular, 36 for pentagrids). Note how for pentagrids, Henry (in this video at 1:50) notes that the lines intersect at either 36 degrees or 72 degrees -- that is, when a line intersects at 72 degrees (2x36) there is one line missing. I suspect that this also plays a part in figuring out why the tiling can't repeat.
      The only bit left really to prove (which is the part I'm not sure on) is proving that you can't make it so that everywhere in a pentagrid where at least 2 lines meet, that there is at least one of those points that does not have 10 spokes (or stated another way, has at least 1 angle between the connecting lines that is 72 degrees).

    • @NotSomeJustinWithoutAMoustache
      @NotSomeJustinWithoutAMoustache Před rokem +14

      @@iwanttwoscoops Rather than clicking away just press L (forward 10 seconds) 6 times to jump forward by a minute. If the sponsorship is still going just press 3 times more, since *most* sponsors are between 60 and 90 seconds iirc. If you actually look at the video buffer rather than the recommended videos list you might sometimes see that not only is the video only halfway through, but, for some channels, they actually go through the trouble of chaptering the ads ie the video literally has the ads' beginning and end timestamped, and marked on the video bar. Lastly, there's also the video hotspots on videos which mark the most replayed portion of a video, and *sometimes* that just so happens to be after the ad. Hope this helps!

  • @stoatystoat174
    @stoatystoat174 Před rokem +77

    The Pattern Collider is fun and free and doesnt ask for any email of details or push cookies at you. Much appreciated Aatish.
    The 6-Fold Stepped Plane (3:27 bottom left) looks like a marching crowd to me. To make it select 6 Fold Symmetry and slide the Disorder to the max right. Cheers Mr Henry

    • @irrelevant_noob
      @irrelevant_noob Před 5 měsíci

      Used to have that pattern on a rug a long time ago, it always mesmerized me into checking how quickly i can switch between seeing a pattern of stairs going "up" in one direction vs in another... or seeing the "inner" bits as concave vs convex. :-)
      PS Had no idea those were the terms i'll eventually use to describe the options, for that kiddo-aged me it was just "bulgy" vs "holey". ^^

  • @lauriethefish2470
    @lauriethefish2470 Před rokem +729

    I love how the music is algorithmically generated. Really fits the video!

    • @finnlyonn237
      @finnlyonn237 Před rokem +214

      It does sound pretty horrible tho

    • @Glendragon
      @Glendragon Před rokem +132

      @@finnlyonn237 and very annoying, I couldn't focus on the content

    • @lonestarr1490
      @lonestarr1490 Před rokem +104

      @@Glendragon Because it kinda repeats, but never actually does *brain boom*

    • @nahometesfay1112
      @nahometesfay1112 Před rokem +115

      @@Glendragon I actually liked it, but I can definitely see how it could be annoying or distracting.

    • @SgtSupaman
      @SgtSupaman Před rokem +30

      @@nahometesfay1112 , it would have been alright if it hadn't been so loud.

  • @phyllostomus
    @phyllostomus Před rokem +244

    Are you familiar with quasicrystals? They are similar to normal crystals, but instead of having a normal repeating unit cell their atoms are-you guessed it-penrose tiled More or less). They were long predicted and made in the lab, but only recently have been found in nature. Could make an interesting video!

    • @DiowE
      @DiowE Před rokem

      I will check it out. [DiowE]

    • @Alexagrigorieff
      @Alexagrigorieff Před rokem +18

      They got the Nobel Prize for quasicrystals

    • @Shr3dward
      @Shr3dward Před rokem +5

      check out the book 'the second kind of impossible'

    • @anon6975
      @anon6975 Před rokem +1

      Hey! That is part of the video where I first heard about this (Veritasium's, 2 years ago) Personally, I thought this had a more elegant mathematical proof but touched on fewer outside implications(Not really a fault of minutephysics, though. Just different styles)

    • @saiganeshmanda4904
      @saiganeshmanda4904 Před rokem

      Wow! I'm really into this now. Could you perhaps share any resources on this?
      I would love to see how far the research has come on this subject...

  • @VJDugan
    @VJDugan Před rokem +228

    The reason why the tiling is aperiodic can be seen more readily when observing the cut-projection method for constructing it.
    The Penrose tiling can be seen as a projection of the 5D integer lattice, Z^5, to a specially chosen 2D subspace -- the squares closest to this plane project onto the plane as rhombuses.
    The a-periodicity comes from the fact that Z^5 is a regular lattice and the 2D plane lies at irrational angles to the Z^5 lattice root vectors.

    • @StackCanary
      @StackCanary Před rokem +11

      Hey it's Dugan Hammock!👋I was just watching your QGR presentation on this very subject a few days ago. I agree, I prefer the cut-projection method for quasicrystal construction but it's neat to see the multi-grid method mentioned here. Quasi-order is so fascinating, especially when investigating physical uses. The fact that quasicrystals can inherit symmetries from their higher-dimensional parent crystals (as in Fibonacci) is intriguing. There was a great paper earlier this year about using a Fibonacci-based quasi-periodic drive system to stabilize a quantum computer against several error modes via emergent dynamics (DOI 10.48550/arXiv.2107.09676 for preprint). I think I'm quasi-obsessed but I'm still trying to wrap my head around some of the QGR stuff you work on. 🤯

    • @VJDugan
      @VJDugan Před rokem +9

      @@StackCanary Thank you! 👋
      I should note that the multi-grid method allows for a much wider variety of tilings than the cut-project method.
      Only certain special arrangements of multi-grids can be re-contextualized into a cut-project scheme from a regular lattice.
      Also there are cut-project schemes which can not be re-contextualized as multi-grid constructions.
      It is also possible to a cut-project of an arbitrary honeycomb or well-behaved tiling -- it's is possible to take a cut-project of a quasicrystal tiling to get a more different quasicrystal tiling in a smaller dimension.

    • @ReasonMakes
      @ReasonMakes Před rokem +13

      My brain exploded trying to read this lol. Sounds awesome but I have no idea where I would even begin with something like that.

    • @astr0nox
      @astr0nox Před rokem +3

      @VJDugan I am not a mathematician, but what you wrote gave me an intuition to why there are no solutions in radicals to the quintic (or higher order) equation (i.e. Abel's impossibility theorem).

    • @haipingcao2212
      @haipingcao2212 Před rokem

      @@VJDugan ΩΩΩΩ

  • @YoshiMario69
    @YoshiMario69 Před rokem +14

    Art and Math are best friends. By themselves a lot of people are intimidated by them, yet they can help explain each other and they both in turn become approachable for everyone ❤❤❤

    • @MrDarren690
      @MrDarren690 Před 6 měsíci

      For sure! Apparently a lot of visual art employs the golden ratio, a mathematical constant

  • @veritasium
    @veritasium Před rokem +410

    Great explanation Henry!

    • @Razorcarl
      @Razorcarl Před rokem +7

      Omg veritasium

    • @BlueAppl337
      @BlueAppl337 Před rokem +5

      ITS VERITASIUM HIMSELF

    • @laxyajena4735
      @laxyajena4735 Před rokem +1

      What only 3 reply 43 like c'mon

    • @desi_bhai_
      @desi_bhai_ Před 11 měsíci +1

      my favourite youtuber here

    • @DevLances89
      @DevLances89 Před 9 měsíci +2

      Bruh only 88 likes that explains why henry doesn't have boring guys in comment sections

  • @rashiro7262
    @rashiro7262 Před rokem +11

    I watched Veritasium's video about Penrose tiles 2 years ago and I couldn't understand why it's never repeating, but your video made it very clear! Thank you!

    • @orstorzsok6708
      @orstorzsok6708 Před rokem

      I suppose - as I remember - that the aim of that video was not to prove this attribute.

  • @grayaj23
    @grayaj23 Před rokem +15

    That was simple and intuitive. And my respect for Penrose only increases the more I know about his work.

  • @Manabender
    @Manabender Před rokem +23

    I opened the Pattern Collider and, for some reason, my first experiment was to play with 3-fold symmetry. Then I shifted the pattern variable down to 0 and got a very nice result that CGP Grey would like.
    Hexagons are the Bestagons.

  • @adamlaceky8127
    @adamlaceky8127 Před rokem +9

    Go back to the beginning, with the green & blue tiles. If you cross your eyes, like it's a stereoscopic image, you can see very well defined straight lines following the pentagrid. Line up two areas with identical patterns, and the pentagrid pops out like it's floating above the Penrose tiles.

  • @TheFinagle
    @TheFinagle Před měsícem

    I love how you acknowledged your explanation doesn't meet the requirements of a proof, but still gives us enough baseline information to follow why without needing a math degree to follow along.

  • @LeoStaley
    @LeoStaley Před rokem +6

    Please do one on the newly discovered a periodic monotile

  • @HershO.
    @HershO. Před rokem +10

    4:49 This was a cool proof! Pretty much the highlight of the video. Also nice to see minutephysics drop.

  • @gimmytomas
    @gimmytomas Před rokem +7

    This is the perfect kind of math/science video we need. Thank you. I wish other channels were as good as yours.

  • @Uathankicks
    @Uathankicks Před rokem +117

    Moorish tilework, that should be pointed out for anyone wanting to learn more. There is also sacred geometry involved beyond the flower of life/golden ratio. In real life the patterns continue across multiple planes(walls and ceilings). It’s incredibly breaktaking to witness in real life. I believe there were other cultures who knew how to create irregular patterns, but the Moors made massive rooms with this stuff.

  • @reidflemingworldstoughestm1394

    Interesting things happen to the (4:29) ratio as the grid goes from a 3-grid, to a 4-grid, to a 5-grid, and so on.
    To see it graphed out, paste this text string
    3gaxkag510
    into the desmos calculator address bar.

  • @arcanine_enjoyer
    @arcanine_enjoyer Před rokem +3

    I like the background audio, it sounds fitting to the topic of something that never repeats itself

  • @DaellusKnights
    @DaellusKnights Před rokem +1

    Penrose is one of my favorites. I only learned about all this when Derek over at Veritasium did his video on this. BUT! I never knew you could scale it up with additional sets! This is absolutely GOD-TIER because I'm planning to tile my living room with penrose tiles, and you just opened up a whole plethora of new tile designs for me? I made my own based on the pentagon, like Penrose did. Now I have to EXPERIMENT!! THANK YOU!! 😻😍💖👍
    Sidenote: previously I knew of penrose via his diagrams related to space-time. So many reasons to be in awe of the dude!

  • @punkkap
    @punkkap Před rokem +7

    Incredible vue work by Mr. Aatish. I will be reading the source of this!
    Thanks for the video Henry!

  • @alvarobyrne
    @alvarobyrne Před rokem +5

    not only the video but the references!!!! well done!

  • @ZacharyVogt
    @ZacharyVogt Před rokem +4

    The premise of this video exactly aligned with my experience. I believed this conclusion because sources I trusted said so, but it was deeply unsatisfying, because their arguments never truly made me understand WHY we KNEW the pattern couldn't repeat. THIS video finally scratched that itch. From unrelated concepts, I eventually absorbed how different rational and irrational are, and new neurons have formed in my brain to link Penrose to my brain's continent of math knowledge.

  • @hankcohen3419
    @hankcohen3419 Před rokem +10

    Thank you! Super cool. I've been interested in Penrose tilings for some time but never knew the underlying structure. I want to use them for marquetry patterns. Now the Pattern Collider gives me a lot more options.

  • @truestopguardatruestop164

    I just read yesterday Penrose’s Wikipedia page and I wondered what that pattern is, but skipped because I was interested in other things. Hugely interesting!

  • @jhawkingsgrey
    @jhawkingsgrey Před rokem +1399

    this video makes me blame my old geometry teacher for not making class this fun

    • @DanielBParada
      @DanielBParada Před rokem +86

      I would’ve killed myself if my 8th grade geometry teacher busted out a grid with 5 axises like I wasn’t already struggling with two lmao

    • @spiderplant
      @spiderplant Před rokem +111

      Largely it's because teachers are paid $50k a year to cover a completely new topic every day on top of crowd control, documentation, assignment creation, grading for up to 120 students every other night, and assessments.
      A content creator maybe needs to make a video every couple weeks at least, can have a team, and can devote most of their time for just that one project.

    • @jhawkingsgrey
      @jhawkingsgrey Před rokem +11

      @@spiderplant yes obviously and yeah teachers should be paid more although i don’t know that everything you said is quite true

    • @spiderplant
      @spiderplant Před rokem +40

      @@jhawkingsgrey As a former educator of 10 years, there's actually more i didn't bother to mention, such as meetings, frequent trainings, conferences, procuring supplies, writing emails, etc.

    • @jhawkingsgrey
      @jhawkingsgrey Před rokem +3

      @@spiderplant oh maybe consider moving to new jersey i have friends who are teachers and my parents are teachers and i know they don’t have to create their own assignments because that’s normally supplied by curriculum director, they don’t have grading that often, etc etc

  • @OneTrueBadShoe
    @OneTrueBadShoe Před rokem +5

    I already knew about this, but I enjoyed the way this video presented it.

  • @cookingforsingles
    @cookingforsingles Před rokem +4

    Super fascinating! I really like this video! It reminds me of my days studying computer graphics!

  • @sarajamal799
    @sarajamal799 Před rokem

    Wow! I was thinking about these patterns the other day! thank you for these amazing videos!

  • @petersmythe6462
    @petersmythe6462 Před rokem +14

    I asked some people about generating noise by stacking waves together at different angles and they said it would end up repeating. I think this really proves that even with very regular angles, frequencies, and amplitudes, that definitely doesn't happen.

    • @pirmelephant
      @pirmelephant Před rokem +5

      Not sure what you mean by angles, but if you want to generate noise, you could do it by overlaying two repeating sound snippets, one with duration 1s and one with sqrt(2)s. This will never repeat because sqrt(2) is irrational. Of course sqrt(2) can't be computed to infinite precision, so it will repeat at some point. But you can delay that point by taking multiple sound snippets where for all durations t_i it is true that t_i/t_j is an irrational number. So for example, 1 s, sqrt(2) s, phi s, pi s etc.

    • @tonylee1667
      @tonylee1667 Před rokem +1

      @@pirmelephant probably meant different phases

    • @jhgvvetyjj6589
      @jhgvvetyjj6589 Před rokem +1

      Noise is supposed to have uniform frequency distribution so even if it is not periodic sound it can still have non-uniform frequencies.

  • @johanngambolputty5351
    @johanngambolputty5351 Před rokem +16

    Damn, I have been playing with minesweeper on voronoi tilings, but using penrose tiling might actually be much better :) I need to try to generate some now

    • @nahometesfay1112
      @nahometesfay1112 Před rokem +3

      Where can I try that? It sounds so cool!

    • @johanngambolputty5351
      @johanngambolputty5351 Před rokem +5

      @@nahometesfay1112 I tried linking once or twice, but I think youtube removed it. Anyway I've put it on itch, its TileGame by JohannGambolputty, may not appear in search right now though...

  • @Dudleymiddleton
    @Dudleymiddleton Před rokem

    Fascinating stuff! I quite liked the marimba music playing in the background! :)

  • @CatFish107
    @CatFish107 Před rokem

    *Keanu voice* whoa. Thanks for this and the link. Going to look into ways of adapting these geometries into rhythms. Similar, yet endlessly changing patterns is the feeling I want to put in my sounds.

  • @WebGrrrlToni
    @WebGrrrlToni Před měsícem

    Thanks you so much for creating this super informative video!!❤❤

  • @heartofdawn2341
    @heartofdawn2341 Před rokem +140

    The binary numbers at the start are also non-periodic. If you count from zero up and put all of the numbers in a single row
    0110111001011101111000...
    You can get an infinite number of repeating segments of any size, but since each number is larger than the previous, the pattern never repeats
    Likewise if you do it with decimal numbers you'll eventually hit 123456789, which is a repeat of the first nine numbers, but it's not periodic as the next number doesn't start with 10..., its 123456790

    • @B3Band
      @B3Band Před rokem +8

      No shit. That was the point of showing it as an example

    • @Konchok_Dawa
      @Konchok_Dawa Před rokem +23

      @@B3Band you don't have to shoot someone down for sharing their thoughts, we're all here to contemplate these things

    • @Konchok_Dawa
      @Konchok_Dawa Před rokem +2

      Im not sure if i understand what you mean by 123456789...do you mean for irrational numbers? Bc you can definitely have 123456789 repeat in an infinite decimal, and that *would* be periodic

    • @suit1337
      @suit1337 Před rokem +1

      ​@@Konchok_Dawa no, he means natural numbers (including zero) expressed in decimal form
      if you write out all decimal numbers in decimal form, you can always add a pattern, that never occured before
      for example
      0123456789 has no repeated pattern
      you can co on
      01231467891011121314151317181920
      if you pick a random digit from form the list, it might occur elsewhere - lets say 1, which occurs multiple times locally (like for example stars in the pentrose pattern)
      you can then extend this pattern by another random digit (before or after) and you are less likely to find this pattern - lets say 12 - we can find den squence 12 multiple times in our list, 2 times to be exact
      now add another digit, 121 - this is there exactly one time
      obviously we can extend this sequence by adding all numbers with 3 digits to have a list von 012345678910111213 ... 999 to find, that 121 occurs multiple times now at least at the edge of 12 to 13 like before and obviously when adding 121
      so when we add another random digit number to the list, we might not find it in our existing list - like the penrose pattern, when you select your pattern to search big enought, it will be unique

  • @PvblivsAelivs
    @PvblivsAelivs Před rokem +6

    I like the darts and kites better. But, the way I have always understood it, given any tiling, you can break the pieces into smaller pieces to create a new tiling or you can build the pieces into larger pieces to make a new tiling. (Well, the tiling might not be new. Some build up into copies of themselves.) But the ratio of the pieces can still be shown to be the golden ratio.

  • @Pouk3D
    @Pouk3D Před rokem

    Thank you, you made me understand better something that I always wondered about.

  • @lilabluestars85
    @lilabluestars85 Před rokem

    I didn't even know about Penrose tiles, but this video explains it beautifully! Thank you 🙂

  • @Royce-Music
    @Royce-Music Před rokem

    The background music also Quasi-Periodic. Awesome little detail! It's so funny to listen to when you actually pay attention to it haha

  • @TGears314
    @TGears314 Před rokem +2

    It’s a wonderful day when minute physics makes a 5+ minute video!

  • @therealEmpyre
    @therealEmpyre Před rokem +10

    For quite some time, I have had this hypothesis that maybe a Penrose tiling does repeat, but you have to go so far to find it that it appears that it never repeats. Now, you have shown me why it is impossible for it to repeat.

  • @kevinotalvares
    @kevinotalvares Před rokem

    Wow the visuals were amazing!

  • @SaveSoilSaveSoil
    @SaveSoilSaveSoil Před rokem

    This is helpful! Thank you very much! Six minutes of my life well spent!

  • @nodroGnotlrahC
    @nodroGnotlrahC Před rokem +8

    Fascinated by the algorithmically generated music, because it bears some resemblances to pieces I have made - (see "Notes From The Analytical Engine" by Beat Frequency on Bandcamp) - please can you post some details about the algorithm.

  • @ferminleon
    @ferminleon Před rokem +3

    I thought the music was going wild on this one, then saw it was algorithmically generated, fun stuff.

    • @ferminleon
      @ferminleon Před rokem

      @Artem Down Well, the result to me is definitely musical, but just wonky enough to grab my attention

  • @WhiskeySour89
    @WhiskeySour89 Před rokem

    This is great, love the channel

  • @jty9631
    @jty9631 Před 2 měsíci +1

    I like shirts with patterns, and I think these penrose patterns would look pretty dope.

  • @JellyMonster1
    @JellyMonster1 Před rokem

    This is one of the best videos I have ever seen. Brilliant!

    • @LeoStaley
      @LeoStaley Před rokem +1

      If you liked this, you'll love veritasium's video on the Penrose tiles.

  • @ThePiMan0903
    @ThePiMan0903 Před rokem +1

    Nice video minutephysics!

  • @adityaprakash5093
    @adityaprakash5093 Před rokem

    Amazing! Thank you!!

  • @AndorianBlues
    @AndorianBlues Před rokem

    Loved the music in this one

  • @bvierville1
    @bvierville1 Před rokem

    Good stuff! Thank you!

  • @RazzyRyan
    @RazzyRyan Před 2 měsíci +1

    I'm redecorating my bathroom soon, and I feel inspired

  • @gaprilis
    @gaprilis Před rokem +1

    Such patterns are not only a mathematical conception but exist in nature, in the materials called quasicrystals, with atoms that never repeat. This discovery awarded a Nobel price to itz finder.

  • @bugoobiga
    @bugoobiga Před 11 měsíci

    great video, subscribed!

  • @Stevobulfer
    @Stevobulfer Před rokem +2

    Hey, was the background music also quasi periodic?? Nice touch! I love it!!

  • @danpatterson8009
    @danpatterson8009 Před rokem

    Excellent presentation.

  • @quanhoang2547
    @quanhoang2547 Před rokem

    Brilliant video!

  • @Fallkhar
    @Fallkhar Před rokem

    Excellent video!

  • @grandexandi
    @grandexandi Před rokem

    Oh my god, content like this is what makes the internet great!

  • @josh34578
    @josh34578 Před rokem +25

    What would the resulting tiling look like if you only used 3 of the 5 sets of parallel lines in the pentagrid?

    • @frojojo5717
      @frojojo5717 Před rokem +12

      Gaps in your tiling?

    • @Shreyy17
      @Shreyy17 Před rokem +3

      Typing something to find the answer

    • @Hendrik_F
      @Hendrik_F Před rokem +4

      Then it wouldn't be a pentagrid anymore, wouldn't it? It would be a grid made of 3 sets of parallel lines, like a triangular grid. But how would the tiling look like?

  • @chandniku1770
    @chandniku1770 Před rokem +2

    I think this is yet another time to remind people that Hexagon are the bestagons!

  • @ajg4Qjg5F4jdrPo
    @ajg4Qjg5F4jdrPo Před rokem +1

    Perfect illustrative music there ;)

  • @jasoncrow6048
    @jasoncrow6048 Před rokem

    Lovely Video!

  • @ranjanjoshi3454
    @ranjanjoshi3454 Před rokem

    Thanks insightful

  • @shellingford9941
    @shellingford9941 Před rokem

    interesting vidéo, thanks for your work ^^

  • @Robpod999
    @Robpod999 Před rokem

    More of this plz!

  • @ForTheOmnissiah
    @ForTheOmnissiah Před rokem

    4:33 the fact that it happened to be the Golden Ratio blew me away. It's awesome that mathematics and science go down some path of research and in the end find something within that is known/discovered.

  • @jamesblackburn8110
    @jamesblackburn8110 Před rokem +1

    BRB gonna draw up a Penrose-crawl for my next D&D session

  • @jonathan.gasser
    @jonathan.gasser Před rokem

    This video was REALLY GOOD

  • @angelodc1652
    @angelodc1652 Před rokem +3

    Here's my interpretation on why they never repeat
    1) Start with 5 wide tiles connected by a corner.
    2) Surround the shape with narrow tiles, by filling every 216 angle with 144 angles, making a decagons
    3) Surround it completely with wide tiles, alternating between filling 144 angles with two 108 angles, and three 72 angles.
    4) Repeat step 2
    5) Repeat step 3, filling 252 angles with 2 72 angles, and filling the sets of three 144 angles by putting 3 72 angles in the middle ones.
    6) Repeat steps 4 and 5 ad inf.
    Since Each band of wide tiles is surrounded both inside and out with narrow tiles, the only time when 5 wide tiles get together is in the center.

    • @irrelevant_noob
      @irrelevant_noob Před 5 měsíci

      But... the bands don't need to be complete... As can be seen at 1:10, there are plenty of "5 wide tiles connected by a corner" shapes in there, it's not just a single one in the whole plane. 🤔

  • @mortimerlojka5912
    @mortimerlojka5912 Před rokem

    Wow...
    By far, the best and most brain-melting video I've seen in ages... !!

  • @op4000exe
    @op4000exe Před rokem +36

    Dunno if it's just me, but the music in the background is just a little too loud for me to properly hear what you're saying without trying too hard.
    I do however get that it's essentially an example of a non-repeating pattern which is very similar, but I don't know if the video would come across a little better if there was a bit larger difference in how loud your voice and the music is.
    Though I suppose people might be less likely to notice the music being different if it was the same, but oh well.
    Great video nonetheless!
    Edit: Spaced out the statement a little to make it easier to read.

    • @rupert7565
      @rupert7565 Před rokem +4

      Agreed. The music is a little to loud here.

    • @ben_burnes
      @ben_burnes Před rokem +2

      I agree too, the music was really obnoxious in this one. Still a super cool video, just... that music isn't a good fit.

    • @KatyaAbc575
      @KatyaAbc575 Před rokem +8

      I didnt even notice there was music in the background. I guess different people have different perception.

    • @AaronOfMpls
      @AaronOfMpls Před rokem +2

      It was fine for me; I didn't really notice it much.
      ...And hmm, I'll have to go back and listen again, to check if the music is quasi-periodic itself. 🙂

    • @murmurmerman
      @murmurmerman Před rokem

      I'm a musician and tend to fixate on musical elements... and I barely noticed the music. Maybe the balance got changed in the 16 hours since your comment got posted?

  • @sabinrawr
    @sabinrawr Před rokem +1

    I was following along pretty well and all was good. Then, out of nowhere, phi appeared. Suddenly, the world made sense.

  • @ooferdoot2429
    @ooferdoot2429 Před rokem

    This helped me understand the grid in dreamscaper and why it always seemed to never make sense it's actually a pentagrid

  • @nataliafidan4222
    @nataliafidan4222 Před rokem

    This channel is educating me
    Who's smol 10 years using mamas account
    And it's insane so thank you!

  • @professeurredstone2134

    So interesting !

  • @haylstorm6
    @haylstorm6 Před rokem

    Love this!!

  • @TheCoBBus
    @TheCoBBus Před rokem

    This would make a cool floor tiling!

  • @linewizard
    @linewizard Před rokem

    Please do a video on hyperbolic geometry and horocycles!!

  • @sigmahunter
    @sigmahunter Před rokem +1

    Superb👍

  • @dntfrthreapr
    @dntfrthreapr Před rokem

    The rationality of this blows my mind!

  • @walterwatson120
    @walterwatson120 Před rokem +1

    ...and the reason a square tiling repeats is because their tiling would be sine of 90°, which is 1.
    That makes sense!
    Thanks, minute physics!

  • @JNCressey
    @JNCressey Před rokem +1

    if I start with the regular square tessellation tiling, then replace one square with an arbitrary asymmetrical design, I also get a tiling that doesn't have global translational symmetry.

  • @nikolaimikuszeit3204
    @nikolaimikuszeit3204 Před rokem

    A lot of math. I like the related aperiodic pattern that one gets as interference pattern of pentagon (heptagon, etc) corners.

  • @seraaron
    @seraaron Před rokem +1

    I love your friend Aatish!

  • @threemooseqateers9689
    @threemooseqateers9689 Před rokem +2

    I have a question I was hoping you could answer. Due to special relativity, if I were to somehow escape the effects of the movement of the galaxy and everything in it, reducing my velocity and the effect of gravity on me to zero, how would I perceive time? Would it stop? Would it travel only slightly slower? If I were to travel to a planet that moved slower relative to Earth, would I experience time differently, and by how much?

  • @cheesepop7175
    @cheesepop7175 Před 7 měsíci

    there is no minutephysics video without a sponsor

  • @2DXYSU
    @2DXYSU Před rokem

    Great stuff. But I especially appreciate it when I discover one of the diminishing number of people who know the difference between fewer and less.

  • @Hardrock1a
    @Hardrock1a Před 8 měsíci +1

    Remember when this was the ultimate in tiling? Now they have found “the hat”, “the specter”.

  • @dogdrovenorth
    @dogdrovenorth Před rokem

    You had me at "patches that are perfect matches".

  • @Cici_Silo
    @Cici_Silo Před 7 měsíci +3

    Couldn't focus on the descriptive dialog because of the DAMN music!

  • @Livi_Noelle
    @Livi_Noelle Před rokem +3

    Fun fact; after massive oral surgery I had Penrose drains that ran from my mouth, through the empty tooth sockets and out through my chin/neck, where I still have a very ugly scar.
    I almost died because I ignored a cracked tooth for a few years. In the course of 4 days, shit went from mild toothache to, "oh God, I can't swallow anymore and my throat is starting to swell shut.
    Take care of your teeth.

  • @olorin4317
    @olorin4317 Před rokem

    I have almost no idea what's going on, but this still has to be one of the best ads I've ever seen.

  • @wizardinthenorthable
    @wizardinthenorthable Před rokem +4

    Who knew someone would discover an einstein just a few months after this video. Maybe good content for a short? Hats and turtle tiles can do it with a single shape.

    • @NonTwinBrothers
      @NonTwinBrothers Před 11 měsíci +1

      And now even a single shape w/o reflections :D

  • @brianarsuaga5008
    @brianarsuaga5008 Před rokem

    I will absolutely accept more minute-physics-math videos.