The Shiny ✨New Shape✨ That Aperiodically Tessellates!

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  • Опубликовано: 29 мар 2023

Комментарии • 420

  • @JustinAion
    @JustinAion Год назад +1166

    My wife wants us to retile our kitchen. She's gonna be SO mad at me...

    • @Ayliean
      @Ayliean  Год назад +261

      Doooooo it!

    • @AlexanderQ689
      @AlexanderQ689 Год назад +30

      I have to remember this idea for my own home

    • @rupert_1491
      @rupert_1491 Год назад +17

      $3.28 says you wont

    • @Epinardscaramel
      @Epinardscaramel Год назад +8

      Oooh there's a Matt Parker bit about that 😅

    • @knittymonstah4978
      @knittymonstah4978 Год назад

      I was about to comment that I want this as a wall in my house 😂

  • @SymbolCymbals2356
    @SymbolCymbals2356 Год назад +421

    I can’t get over how they called it a hat when it’s 100% a t-shirt

    • @liubov2341
      @liubov2341 Год назад +11

      I was thinking the exact same thing! It IS definitely a t-shirt

    • @c2h680
      @c2h680 Год назад +11

      Obviously it’s a pair of boots.

    • @SymbolCymbals2356
      @SymbolCymbals2356 Год назад +7

      @@c2h680 a pair of boots makes sense too!

    • @Tumbolisu
      @Tumbolisu Год назад +7

      @Scott's Precious Little Account 2:21 "They call it the hat."

    • @mastpg
      @mastpg Год назад

      .... proportionally, more like a football jersey.

  • @michaeljmcguffin
    @michaeljmcguffin Год назад +283

    This is such a good, engaging, visual, quick explanation of this topic!

    • @Ayliean
      @Ayliean  Год назад +28

      Thank you! That’s all I aim for 🥰

    • @timmy18135
      @timmy18135 Год назад +2

      @@Ayliean Like how vihart would do it

    • @rare.and.important.content
      @rare.and.important.content Год назад

      I totally agree. @@Ayliean you have great talent for this!

  • @drdca8263
    @drdca8263 Год назад +343

    This is maybe kind of pedantic (and something you surely understand, I’m just saying ~~just in case some viewers might not catch it~~ actually no, the real reason is just because I am compelled to be pedantic), but I want to note that the difficult thing isn’t a set of tiles which *can* be used to tile the plane in an aperiodic way, but rather to find such tiles which also *cannot* tile it in a periodic way.
    If your tiles are 2x1 rectangles, you can take the obvious tiling where you group them into squares, and then tile the squares in a periodic way, but the rotate just one of the squares. The resulting tiling of the plane with the rectangular tiles is not periodic, in that it doesn’t exhibit translational symmetry.
    So the difficulty isn’t “tiles which can tile the plane aperiodically”, but “tiles which can only tile the plane aperiodically”

    • @harshsrivastava9570
      @harshsrivastava9570 Год назад +45

      honestly, oftentimes it's useful to have "pedantic" (rigorous) expressions, just for the maximum precision in communication. so, thank you drdca.

    • @tomasstana5423
      @tomasstana5423 Год назад +40

      No need to call this pedantic. It is actually quite important detail, thanks for clearing this out.

    • @sakesaurus1706
      @sakesaurus1706 Год назад +2

      I didn't realize. If i paused and thought about it then I'd see this coming but I didn't.

    • @Mecharnie_Dobbs
      @Mecharnie_Dobbs Год назад +5

      ​@@massimomoro5895 It covers the plain without overlaps or gaps. It meets the definition of tiling that we were given at the start.

    • @drdca8263
      @drdca8263 Год назад +3

      @@massimomoro5895 linear symmetry is just symmetry under some group of translations, which is broken by the tiles that are turned the other way.
      It is still a tiling because it partitions the plane into copies of the tile which only overlap at the boundary.

  • @ExecutorElassus
    @ExecutorElassus Год назад +360

    I will never understand why hardware/home-improvement stores don't sell various kinds of aperiodic tiles. I'm sure I'm not the only one who'd absolutely tile a floor or a backsplash or a whole bathroom with them.

    • @donaldasayers
      @donaldasayers Год назад +85

      I wanted to sell regular pentagonal wall tiles under the trade name 'Futile'. 😀

    • @MaxG628
      @MaxG628 Год назад +31

      Perhaps these shapes only tile when mathematically perfect, and real-world imperfections prevent practical use? Then again, I’ve played with physical Penrose tiles and it seems to work.

    • @justin2039
      @justin2039 Год назад +45

      Grout lines would actually make it easier, not harder I suspect.

    • @AmandaComeauCreates
      @AmandaComeauCreates Год назад +10

      Good idea for someone who can 3d print in a material that can be kilned to tile durability :D or recycled plastics sealed against offgassing!

    • @KSignalEingang
      @KSignalEingang Год назад +16

      I imagine you could make a mold and use colored concrete for outdoor tilings. In fact, I plan to try!

  • @karlwaugh30
    @karlwaugh30 Год назад +70

    This has been my favourite recent development in a long long time! I tried reading the paper but it kinda floated past me (I'm a lapsed professional mathematician). Would really love to see a breakdown of how it kinda works and why and what the continuum you mentioned is.

    • @JohnDoe-ti2np
      @JohnDoe-ti2np Год назад

      Look for the National Museum of Mathematics RUclips video, "A Hat for Einstein".

    • @pirobot668beta
      @pirobot668beta Год назад

      I broke the Game.
      Regular Triangle, in 24 tiles.
      ruclips.net/user/shortsdnGtToFlUFE

  • @TheNethIafin
    @TheNethIafin Год назад +52

    Very good content!
    The fact that this tiling uses mirror image for some tiles feels like a cheat on "just one tile" pattern 😅. Guess we can call it 1.5 tiling pattern

    • @rosiefay7283
      @rosiefay7283 Год назад +10

      This is not considered cheating. Reflecting has always been allowed.

    • @TheNethIafin
      @TheNethIafin Год назад +3

      @@rosiefay7283 I understand that it was always allowed, and I suspect that doing infinite tiling without reflection or second piece is probably impossible

    • @keithbellic2629
      @keithbellic2629 Год назад +10

      An A press is an A press, you can’t call it a half.

    • @francogonz
      @francogonz Год назад

      Yeah but, if you have ∞ pieces of this shape 3d printed, you can cover an entire plane. As an tangible object you can actually do it as a unique tile

    • @PhilBagels
      @PhilBagels Год назад

      Yeah. Penrose tiles do not need to be flipped. So both these and Penrose's use two tiles each.

  • @robbiekavanagh2802
    @robbiekavanagh2802 Год назад +7

    The fact that you can flip the shape over feels like a bit of a cheese to me, there ought to be an asterisk over 'aperiodic monotile' (*)

  • @vincent-danielgirard4873
    @vincent-danielgirard4873 Год назад +13

    This is the first engaging video I see on this monster of a discovery! I'm SOOOOO surprised Matt Parker / Numberphile / Any other science channel haven't made a video on it yet. I was about to paint penrose tilings in my room, but guess I'm switching up now!!!

  • @flamencoprof
    @flamencoprof Год назад +9

    I just knew Penrose would get mentioned. In the early Eighties I read in Scientific American about tiling and fractals. I tried programming fractals on a Commodore 64. I was still not prepared for when in 1996 I visited Spain and saw the awesome tiling of places like El Alhambra. I even added a painted pattern to my bathroom walls when I got home.
    I got low marks for Maths at school, but have retained a life-long interest for another 50+ years. Even in about 2000, I was still creating patterns in MS Paint that could be tiled on my work PC desktop, in work idle time.

    • @sminstudios
      @sminstudios Год назад

      I fantasize about MC Escher seeing Guastavino tiles/tesselations/vaults but he resisted getting into the Builders’ realm.

  • @thebooknerd5223
    @thebooknerd5223 Год назад +4

    This reminds me so much of a Vi Hart video! Those videos entertained me for a large portion of my childhood. I’m glad I found you and hope to enjoy more of your content!

  • @jamestarrou3685
    @jamestarrou3685 Год назад +11

    the part about an periodic element being structured as an aperiodic tiling was interesting!

  • @MathVisualProofs
    @MathVisualProofs Год назад +5

    This is EXCELLENT work. What a great video. Thanks!

  • @57z
    @57z Год назад +6

    I find it interesting that the tessellation pattern somewhat reminds me of a Mandelbrot fractal

  • @Nijht
    @Nijht Год назад +2

    Your voice is so smooth to listen to, your enthusiasm so endearing, and the topic so interesting, that when the video ended I was hit with a mild shellshock. I was ready to just sit and listen for another twenty minutes.

  • @Lou.B
    @Lou.B Год назад +1

    Fascinating! Some of those patterns are very reminiscent of Escher.

  • @f.g.5967
    @f.g.5967 Год назад

    The proper response to “what’s the use of that” is a punch straight to the guts.

  • @Quasarbooster
    @Quasarbooster Год назад +9

    I remember seeing a numberphile video awhile ago that showed a tile that could do this, but it has multiple disconnected pieces. Great to know they found a single piece that can do it (albeit with some being reflected)

    • @Tumbolisu
      @Tumbolisu Год назад +1

      I heard that it's impossible to have such a shape that is both connected and never needs to be reflected.

    • @swordfishxd-
      @swordfishxd- Год назад

      @@Tumbolisu The specter tile

  • @Preset1
    @Preset1 Год назад +1

    Love the way you engagingly yet simply communicated mathematic principles which were able to be understood, especially since I did terribly at school

  • @uitham
    @uitham Год назад

    i like how instead of talking you telepathically transmit thoughts to me

    • @uitham
      @uitham Год назад

      Terrific, tantalizing telepathy: transferring thoughts, transcending traditional talk.

  • @cptnbara
    @cptnbara Год назад

    This was really interesting! It was a lot of information provided very briefly, but it never felt overwhelming. Brilliant and engaging, thank you!

  • @shillinhite3911
    @shillinhite3911 Год назад

    I'm really stoked for the math fandom right now, you're all over here doin stuff--gold star!

  • @serhancinar5218
    @serhancinar5218 Год назад

    Such a fantastic subject explained in such a fantastic video... Simply beautiful

  • @AnneloesF
    @AnneloesF Год назад

    This makes me very happy! Thank you for sharing this news so clearly and enthusiastically! Congratulations to the team of discoverers and to the giants whose shoulders they stand on!

  • @donaldasayers
    @donaldasayers Год назад +3

    It is a little bit of a cheat as there are two tiles in use, the tile and it's mirror image. For me that's pushing the definition of 'monotile' a little.

  • @fbrand-vp4oy
    @fbrand-vp4oy Год назад

    amazingly good explanation of such a complex subject,
    thank you so sooooo much for this great effort you put into it!

  • @Artsyca
    @Artsyca Год назад +1

    Kudos! A very informative, concise and entertaining explanation.

  • @PaweFiga
    @PaweFiga Год назад

    I love this video. The topic, the spirit of Ayliean, This is is such good presentation visually. 1000 out of 10

  • @tmagrit
    @tmagrit Год назад

    Gorgeous in so many ways...

  • @moralboundaries1
    @moralboundaries1 Год назад

    Those freehand tile illustrations are awesome. I might give that a go! Thanks for the cool content!

  • @amoghgokhale2366
    @amoghgokhale2366 Год назад +1

    Finally someone who explains tessalation is a easy to understand way. Great Video!!

  • @Dr_KW
    @Dr_KW Год назад

    Wow. This is a lovely and succinct way of explaining a topic that can be so difficult to visualize!!

  • @19TheChaosWarrior79
    @19TheChaosWarrior79 Год назад +1

    Another fantastic video. Brings a whole new meaning to ' a night on the tiles'

  • @outwalkingthebird
    @outwalkingthebird Год назад +2

    this video is so high quality, informative and entertaining you managed to get the big three I LOVE IT great job

  • @johnodonnell2495
    @johnodonnell2495 Год назад

    Super video! Easy to understand and fun! Great job

  • @malaineeward5249
    @malaineeward5249 Год назад

    I absolutely love that "the hat" tiles out in a fractile pattern! 🥰

  • @nathanielhellerstein5871
    @nathanielhellerstein5871 Год назад +1

    Truly groovy! But two quibbles: I don't think it's a hat; turn it upside down and you'll see a T-shirt. Also, as others on this thread note, if you have to turn the tile backwards, then that's two tiles, sort of.
    How do you do the tiling?

  • @vl8822
    @vl8822 Год назад

    Just wanted to say this was a lovely video! Great work, I love this kind of stuff!

  • @heighRick
    @heighRick Год назад

    Thanks for the video Ayliean, helps a lot!

  • @sweetdeemdd9678
    @sweetdeemdd9678 Год назад

    You are an incredible teacher and video editor. Watched 4 videos on this and still did not understand what was being discussed fully. After this video I get it and you made it so simple and fun. Cheers

  • @laylahassomethingtosay
    @laylahassomethingtosay Год назад

    Whoaa, this is super cool!! Thanks for making such a great video!

  • @75blackviking
    @75blackviking Год назад

    This concept is sooo badass. I love the little cardboard TV, too.

  • @qy9MC
    @qy9MC Год назад

    Very nice video! Love it.

  • @disconnectica
    @disconnectica Год назад +3

    Next question: can it be done with one tile WITHOUT allowing reflections?

  • @Xephyra
    @Xephyra Год назад

    The happiness this gives me is unsurpassed. An aperiodic monotile. This is peak elation.

  • @prilep5
    @prilep5 Год назад

    Thank you for great explanation

  • @philipegoulet448
    @philipegoulet448 Год назад

    Very well presented!

  • @balbarard4041
    @balbarard4041 Год назад

    love this video! great explanation

  • @littlewyzard
    @littlewyzard Год назад

    it looks like such ha simple shape at first glance! it makes you wonder how many times this shape has been created by just pure chance

  • @kaidenschmidt157
    @kaidenschmidt157 Год назад

    I thought of this channel when I saw the discovery. I was sure this would make some great math art

  • @electronicgarden3259
    @electronicgarden3259 Год назад +5

    Wow! Such a seemingly simple thing and yet it took years to come up with a single tile solution.
    But even if it is the same shape you still have to use it mirrored. Isn't that two tiles then?
    Still impressive to be able to cover a surface with just one shape AND the pattern NEVER repeats. Incredible!
    The connection with the aluminum alloy was interesting. There's math everywhere 😊

    • @thirddiversiondeep
      @thirddiversiondeep Год назад +1

      Aluminium*

    • @electronicgarden3259
      @electronicgarden3259 Год назад

      @@thirddiversiondeep Sorry, English is my second language.
      Is it only called aluminum in American English? It's aluminium in Swedish.

    • @ttmfndng201
      @ttmfndng201 Год назад +5

      ​@@electronicgarden3259 Aluminum is used in american english and aluminium in british english, but both spellings are correct.

    • @electronicgarden3259
      @electronicgarden3259 Год назад

      @@ttmfndng201 Thanks. I like the European way 😀

    • @thirddiversiondeep
      @thirddiversiondeep Год назад

      @@electronicgarden3259 Correct!👍😀

  • @user-hh6xp9dv8c
    @user-hh6xp9dv8c Год назад

    THANK YOU SO MUCH FOR EXPLAINING THIS I HAD SO MANY QUESTIONS I LOVE U

  • @kal7498
    @kal7498 Год назад

    this is so interesting to watch,, i love it!!

  • @paperstars9078
    @paperstars9078 Год назад +1

    are there more videos coming like this, because this is gold!

  • @jonnyhifi
    @jonnyhifi Год назад

    A superb video ! Well done !

  • @abhishekk4194
    @abhishekk4194 Год назад

    Mindblowing. I have never paid attention to floor tiling patterns.

  • @sidneyn1366
    @sidneyn1366 Год назад

    I'm not good at math (yet) but boy am I obsessed with how amazing and satisfying it is. I loved this video!

  • @mavigogun
    @mavigogun Год назад

    Well done- thanks for that.

  • @loneshine
    @loneshine Год назад

    Never would've guessed how fascinated I would be by this-- thank you!

  • @hullabulla
    @hullabulla Год назад

    Great video!! You earned a subscriber! Would be awesome to go down into the more math behind it as well or how it works

  • @pmnt_
    @pmnt_ Год назад

    this is the first video i saw from this channel and i have to say - and i mean that as compliment - your style reminds me of vihart.

  • @MrFranklitalien
    @MrFranklitalien Год назад

    thank you for sharing, it made my day :)

  • @liliththeoshwaire7698
    @liliththeoshwaire7698 Год назад

    This channel deserves more subscribers.

  • @yisus.avocado
    @yisus.avocado Год назад

    Great explanation of such an interesting topic :D

  • @wait4tues
    @wait4tues Год назад

    This is peak RUclips for me. Thanks for making interesting content.

  • @NonTwinBrothers
    @NonTwinBrothers Год назад

    Getting New-Vihart vibes from this vid. Keep up the good work :D

  • @rerun3283
    @rerun3283 Год назад

    I have been wondering about this for years and had no idea what to even look up. ❤

  • @charleslambert3368
    @charleslambert3368 Год назад

    Love how Escherian your desk ornaments are

  • @kikijewell2967
    @kikijewell2967 Год назад

    Reminds me of the book, Archemedes Revenge - a fun little book of lots of little puzzle histories.

  • @ZenQuagga
    @ZenQuagga Год назад +3

    I mean yeah, it's a hat, but I think it looks the most like a tee shirt that's been half tucked 😂 I've been interested in topology and hyperdimensional geometry since middle school. I am so excited to see new mathematical discoveries being made! The larger tiling patterns look VERY fractal-like, is the correlation meaningful or pareidolic?

  • @Ry-gh4xe
    @Ry-gh4xe 7 месяцев назад

    I think this might be my new favorite channel! 😃

  • @Kram1032
    @Kram1032 Год назад +1

    what's crazy is that this is such a simple idea. It really just combines the hexagonal and trigonal tiling and cuts out a kinda arbitrary but rather simple shape. (That said, this connection to those decidedly periodic tiles makes it, in a sense, less aperiodic than it could be. Patterns end up looking like hexagonal tilings with some variation. It feels less aesthetically pleasing, imo, than the penrose tiling)
    Of course the next question is going to be what if reflection isn't allowed? Rotation and translation only? Still possible, or is the reflection a necessary condition?

  • @neuzd
    @neuzd Год назад

    Come on! That's the Julia set! Amazing.

  • @VeganofCourse
    @VeganofCourse Год назад

    Amazing. Great video.

  • @nicholaspizzi710
    @nicholaspizzi710 Год назад +2

    What software are you using? I’m a chemist, and am studying water structure that follows 5-fold symmetrical quasi-crystal structure. That this shows us a spectrum of shapes that can tile aperiodically, makes me think there are other molecular structures that can be built, or already exist, and may explain certain phenomena like glass structure. So, which software is it?

  • @cyrilio
    @cyrilio Год назад

    Very cool fact about the Penrose tilling right at the end.

  • @simonkhouryAU
    @simonkhouryAU Год назад

    great explanation! very cool

  • @lindakilmer2548
    @lindakilmer2548 Год назад +1

    That’s so cool! Is it related to fractal geometry?

  • @konstantinavalentina3850
    @konstantinavalentina3850 Год назад

    New to your channel (subscribing now); I thought M.C. Escher did quite a number of tesselations; some monotile, and some others dual tile?

  • @ytidentity
    @ytidentity Год назад

    Nice ! I was wondering ... are there non repetitive tilings that cover the surface of a sphere ?

  • @md-sl1io
    @md-sl1io Год назад +4

    wouldnt quadrilleteralls tile the plane aperiodiclly if u lined them up like normal then shifted each column along by a random amount

    • @Autoskip
      @Autoskip Год назад +3

      Absolutely - the actual search was for tilings that can _only_ tile the plane aperiodically. Penrose achieved that by basing his tiling on regular pentagons, which cannot (normally) tile, creating a tiling that doesn't abide by the normal rules of tiling. I don't (yet) fully understand the hat tiling, but the penrose tiling can trivially be made to be rotationally symetric, but if it repeated, then those rotational symetry points would repeat too, and you'd be able to find more points by rotating one point 72° around another point - but if you try that a few times, you'll find out that they'll never line up with each other.

  • @meowmeowsaymeowmeow
    @meowmeowsaymeowmeow Год назад +1

    Great video. I would love to know how much shapes are created/discovered. There's more to it than trial and error, but what? 🤔 Would love to know!!

  • @themexyeti
    @themexyeti Год назад

    I remember watiching the Veritasium video about the penrose tesselation and I was facinated by it, having a one shape, one color and no funny tricks, for an aperiodically tesselation just blow my mind

  • @make.it.rainer
    @make.it.rainer Год назад

    I’m here to tell you that this was one of the greatest videos I’ve ever seen. I’m almost embarrassed by how enthralled I was in a video about floor tile 😅

  • @kylelawson
    @kylelawson Год назад

    So fun! Thank you

  • @floatingpiss
    @floatingpiss Год назад

    Hi, this is a really cool discovery, sources or doi links in the description would be cool

  • @MrYeyit
    @MrYeyit Год назад

    Would have appreciated links in the description -- yay new shape!

  • @lissythearchitect
    @lissythearchitect Год назад

    I really like the 'we haven't finished maths yet'.
    I recall as a math Teacher's Assistant talking to a few of my students about the math classes I was taking in grad school. One of them was shocked when I talked about math research, because they apparently thought maths was 'done'.

  • @platykurtic5510
    @platykurtic5510 Год назад +1

    Oh wow. There was the Taylor-Socolor aperiodic monotile, but it was disconnected, which was less than satisfactory. This is a super nice monotile.

    • @rosiefay7283
      @rosiefay7283 Год назад

      The problem with it was that it isn't one tile. Being disconnected means that it isn't one tile.

    • @platykurtic5510
      @platykurtic5510 Год назад

      @@rosiefay7283 That is a fair assessment.

  • @cheyenne1309
    @cheyenne1309 Год назад

    Whatever branch of math involves fractals tesselations and things of this nature is exactly where I need to be

  • @anonymous15432
    @anonymous15432 Год назад

    This immediately reminded me of the dragon curve fractal from Jurassic Park

  • @reecedeyoung6595
    @reecedeyoung6595 Год назад

    Your tattoos are so cool!!

  • @typo691
    @typo691 Год назад

    Got a link to a paper or maybe other source for that aluminium alloy fact? Probably the most interesting thing I've heard in a while

  • @IndyJay53
    @IndyJay53 Год назад

    "We haven't finished maths yet." I love it

  • @LeoStaley
    @LeoStaley Год назад

    No idea who you are, but I've been looking for an explained on RUclips to talk a oh this since it was announced, and you're the first I've seen.

  • @xicufwm
    @xicufwm Год назад +1

    1:58 do you still have room in the other arm for the hat tiling? That one deserves its own tattoo!

  • @LinkEX
    @LinkEX Год назад

    Board Game Designers are probably having a field trip since this came out.
    Both figuratively, and (semi-)literally, on the new Einstein board game tiles they presumably now experiment with.
    Especially the implications of two-sided tiles with different properties should make for interesting game mechanic, instead of the familiar hex tiles or square tiles.
    I'm thinking of games like Carcassonne in particular)

  • @wafikiri_
    @wafikiri_ Год назад

    There are infinitely many ways of getting periodic tilings with regular pentagons and rhombuses, and they can be homogeneously but anisotropically deformed so that pentagons lose their regularity and rhombuses become rhomboids or squares.

  • @IHaveaPinkBeard
    @IHaveaPinkBeard Год назад

    My mind is so totally blown now.

  • @miles_quartz
    @miles_quartz Год назад

    I don't know why this was reccomended to me, this is so outside of my realm of knowledge but it's really cool so I'd love to know more :o