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Mathematical Lego Sculptures 185

Posted by michael from the too-much-time-on-your-hands dept.
Daedalus_ writes "Some guy has created mathematical surfaces (mobius strips, klein bottles, etc) out of Legos. He also has some other interesting creations (such as Dilbert figurines and a Hoberman Sphere)."
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Mathematical Lego Sculptures More

Mathematical Lego Sculptures

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  • One of those snakey thingeys that have all those sections you twist go back into the container?

    I could NEVER figure that out.
  • Does this mean that the lego representation of a surface integral is not far behind?

  • Holy crap! (Score:5, Funny)

    by TheCyko1 ( 568452 ) on Tuesday July 02, 2002 @10:48PM (#3812094)
    Lego people can walk sideways on buildings?? We must make them our leaders!

  • And the conjugate... (Score:3, Interesting)

    by digitalhermit ( 113459 ) on Tuesday July 02, 2002 @10:51PM (#3812104) Homepage
    Creating legos out of mathematical surfaces... (Use POVRay to render this :D).

    #include "colors.inc"
    #include "textures.inc"
    #include "metals.inc"

    camera {
    location
    look_at
    }

    plane { , -1
    pigment {
    checker color Red, color Blue
    }
    }

    light_source { color White} // example of object unions

    #declare lego=union {
    box {
    ,

    }

    #declare cyl1=cylinder {
    , .5
    }

    object { cyl1 }
    object { cyl1 translate }
    object { cyl1 translate }
    object { cyl1 translate }
    object { cyl1 translate }
    object { cyl1 translate }

    texture { Glossy
    pigment { Red }
    }

    }

    object { lego }
    object { lego
    translate
    rotate 20*y
    }

    • Re:And the conjugate... (Score:4, Interesting)

      by digitalhermit ( 113459 ) on Tuesday July 02, 2002 @10:56PM (#3812121) Homepage
      Let's try this again...

      #include "colors.inc"
      #include "textures.inc"
      #include "metals.inc"

      camera {
      location < 0, 8, -8 >
      look_at < 0, 1, 2 >
      }

      plane { <0, 1, 0>, -1
      pigment {
      checker color Red, color Blue
      }
      }

      light_source { <2, 4, -3> color White} // example of object unions

      #declare lego=union {
      box {
      <6, 0, 0>,
      <0, 2, 4>
      }

      #declare cyl1=cylinder {
      <1, 0, 1>,
      <1, 2.5, 1> .5
      }

      object { cyl1 }
      object { cyl1 translate < 2, 0, 0> }
      object { cyl1 translate < 4, 0, 0> }
      object { cyl1 translate < 0, 0, 2> }
      object { cyl1 translate < 2, 0, 2> }
      object { cyl1 translate < 4, 0, 2> }

      texture { Glossy
      pigment { Red }
      }

      }

      object { lego }
      object { lego
      translate < -6, 0, 5 >
      rotate 20*y
      }

  • Figure Eight Knot (Score:5, Insightful)

    by abigor ( 540274 ) on Tuesday July 02, 2002 @10:52PM (#3812108)
    That is totally amazing. And for what it's worth, I think it's a worthwhile use of his time (not that my opinion on how someone uses their time matters, but whatever). I don't know, to me for some reason non-trivial acts of creation like this seem to touch whatever it is to be human -- our creative endowment is one of our signature traits, I think. What impulse would drive this sort of creative urge, to create beautiful mathematical shapes out of Lego, of all things? Whatever it is, it's mysterious, and it wasn't a waste of time. That figure eight knot is incredible.

  • Wow.... (Score:5, Funny)

    by RaboKrabekian ( 461040 ) on Tuesday July 02, 2002 @10:54PM (#3812112) Journal
    Very, very cool.

    Now show me a hypercube and I'll be really impressed.

    • Re:Wow.... (Score:2, Interesting)

      by Medevo ( 526922 )
      The Only way humans can view a hypercube (a 4d cube) is using 3D representation. The basic idea behind this is similar to how we can make 3d looking things on our 2d monitors. Since humans find it next to impossible to visualize hypercubes, we would need to program a computer with enough knowledge of 3d and 4d shapes (and how to represent them).

      Even if we did this the BEST way to view a hypercube would be either to go to the 4th dimension to look at one, or have a creature from the 4th dimension come here and make a 3d representation of on.

      Don't think this is happening anytime soon.

      Medevo
      • Yes, I know - I was making a joke.

      • Re:Wow.... (Score:2, Funny)

        by Anonymous Coward
        or you could just run xlock -mode hyper.

      • Hypercube (Score:3, Interesting)

        by magicslax ( 532351 )
        Even if we did this the BEST way to view a hypercube would be either to go to the 4th dimension to look at one, or have a creature from the 4th dimension come here and make a 3d representation of on.

        ..and the second best way is right here. [dogfeathers.com]

      • That doesn't stop him from building a klein bottle and so on.
      • You try to make a little joke, but there is always some Poindexter out there who takes you literally and points out your "mistake" in mind-numbing detail...
      • Let's use time as our 4th dimension. Imagine a cube that appears and then disappears in an instant. That's a 3D cube. Now stare at a cube for a few seconds.

        That's a hypercube.

        A 4D being would see the difference instantly. The 3D cube would seem kind of "flat" next to the other one.

    • Re:Wow.... (Score:4, Funny)

      by Hollinger ( 16202 ) <michael AT hollinger DOT net> on Tuesday July 02, 2002 @11:35PM (#3812232) Homepage Journal
      That's easy. Take a 4-cube. Pass it through 3-space, and what you'll see is an infinitely small cube at the point in the center of the 4-cube which will then grow to the cross-sectional size of the 4-cube, and shrink back down. Not too hard to wrap your head around. Tesseracts are a totally different matter...

      • Re:Wow.... (Score:5, Informative)

        by ErfC ( 127418 ) on Wednesday July 03, 2002 @01:47AM (#3812540) Homepage
        That's easy. Take a 4-cube. Pass it through 3-space, and what you'll see is an infinitely small cube at the point in the center of the 4-cube which will then grow to the cross-sectional size of the 4-cube, and shrink back down. Not too hard to wrap your head around. Tesseracts are a totally different matter...

        I disagree. That nicely describes what happens with a sphere, but not so much with a cube.

        I guess it depends on how it's passing through 3-space. The best way to imagine this stuff is to imagine a 3-D object passing through 2-space. If you pass the cube through corner first, you'll get something like what you describe, except the cross sections will be triangular most of the time. Edge on, you'll get rectangles.

        Face-on, your 2-space will see nothing until the 3-cube hits it, then the 2-space will see a square just sitting there until the 3-cube is all the way through.

        What's the difference between a tesseract and a 4-cube? According to Eric Weisstein, it seems they're the same thing [wolfram.com].

        • You know, you're perfectly correct. I defer to you. You know, it's too bad you can't append old posts...

      • Imagine a 2 dimensional person seeing a 3 dimensional cube pass through his space. If the flat surface of the 3d cube is parallel with the 2d universe, the 2d person will simply see a square miraculously appear before him, hover for awhile, and then disappear. If the surface of the 3d cube is not completely uniform the 2d person might see the surface of the square "morph" a little. Similarly, if a 4d cube passed through our 3d universe, we would see a cube miraculously appear and then, after a few moments, disappear.

        Things become interesting if you pass the corner of the 3d cube through the 2d universe first. The 2d person would see tiny triangle appear before him that grows larger and larger, until you hit the next corners and things become complex, especially if the cube entered at an angle. Eventually you'll get back to a floating triangle that shrinks down to nothingness. Similarly, a 4d cube going through our universe will appear as a 3 sided growing pyramid at first.

        Another way to imagine a 4d cube is to think about what its shadow would look like in our universe. The way to do that is to take a 3d cube and project its shadow on a wall. Straight on from the light source it looks like a square. Move it around and see how it morphs. Now image a 4d person was projecting the shadow of a 4d cube onto our universe. Straight on we would have a 3d cube. If he moved the cube around, various corners of the 4th dimension would "morph" out of the flat sides.

        When we talk about seeing a hypercube we usually talk about the shadow of a transparent cube, where you just see the connecting lines. This would give you a cube inside of a cube with the corners of the inner cube connected to the corners of the outer cube.

    • Re:Wow.... (Score:4, Interesting)

      by NaDrew ( 561847 ) <nadrew@gmail.com> on Tuesday July 02, 2002 @11:49PM (#3812267) Journal
      I was hoping to see a Calabi-Yau space [thinkquest.org], myself. How many 1x3's would that take?
    • If he did construct a hypercube, he'd probably spontaneously transcend to a higher plane of existance as soon as he put the last brick in place.
      • he'd probably spontaneously transcend to a higher plane of existance

        ...where the sky is a hyperintelligent shade of blue, no doubt.

  • Other lego sculpture sites (Score:5, Informative)

    by Juhaa ( 588855 ) on Tuesday July 02, 2002 @10:56PM (#3812120)
    I love Andrew Lipson's Math site, thought it was on slashdot for a while. If you like to see other such sites check out Eric Harshbarge's [ericharshbarger.org] Lego page (cool stuff like wedding cakes and skyscrapers), Henry Lim's totally awsome lego sculptures [henrylim.org], he's even got Natalie Portman (Not naked, and next to the petrified beethovan). BTW, Eric's got a very interesting page on on San Mononoke [ericharshbarger.org] (more on those [about.com]).
    • It is not really Natalie Portman it is Queen Amidala. I feel cheated, Queen Amidal looks more like a bad set of curtains than Natlie Portman.

      On his web page he even titles the sculpture.
      Queen Amidala
      "My apologies to Ms. Portman"

      Now this page is more like it (no lego though)
      http://www.natalie-portman.net/pictures.h tm

      --
      "This isn't a Troll"
      Of course a troll would say that
  • Wait a second, isn't this idea very very close to the Oop! idea in Douglas Coupland's "Microserfs"?
  • I would be impressed with a Dyson Sphere [d.kth.se] out of legos. That would be cool.
    And you could have a little Scotty Lego charachter next to a crashed shuttle craft on the surface.
  • I'm not the only person that realizes that a klein bottle can't be made with lego? Or with anything that we know of...
    klein bottles can't really be represented in three dimensions...
    • It cannot be embedded in R^3, but it sure can be represented in r^3. See here [umn.edu]

      It's like saying you cant represent a cube in R^2, or any other 3d shape we commonly see represented on our computer monitors and tv screens, which are 2d last time I looked :)

    • I'm not the only person that realizes that a klein bottle can't be made with lego? Or with anything that we know of...
      klein bottles can't really be represented in three dimensions...

      Um, (claps one hand against belly or other skin-coated surface) you must have overlooked these.
      http://www.kleinbottle.com/ [kleinbottle.com]

      Although I cannot figure how as it is the first hit when I GOOGLE a [ Klein Bottle ] search. There is even a Klein Coffee cup! Now stop being silly and order one for goodness sake.

  • I love it (Score:4, Funny)

    by nfras ( 313241 ) on Tuesday July 02, 2002 @11:20PM (#3812188)
    On his other page I particularly liked the machine for switching itself off. Mind you, he'd need to be careful, he might be breaching Microsoft's patent on Windows.

    • Re:I love it (Score:2, Funny)

      by napa1m ( 154836 )
      I think he's safe. Most of my windows machines won't even switch themselves off! "Windows is shutting down" my @ss..

      I obviously need a small lego machine to pull the plug out of the wall every time it locks up... hmmm

  • Oh yeah? (Score:3, Funny)

    by Anonymous Coward on Tuesday July 02, 2002 @11:20PM (#3812190)
    I can make a near-perfect rectangular parallelepiped out of single Lego brick. Top THAT!

  • Mirror Site (Score:3, Informative)

    by zerocool^ ( 112121 ) on Tuesday July 02, 2002 @11:23PM (#3812198) Homepage Journal

    Mirror site up.

    www.netmar.com/~will/lego [netmar.com]

    Disclaimers:
    1.) Not my work, I don't claim any of it.
    2.) I didn't get the .DAT files.
    3.) I know it's not slashdotted yet, just preparing/ karma whoring.
    4.) If it does get slashdotted, and everyone starts testing my load balancing, why not sign up for hosting at the same time? We're running a no setup fee promotion at the moment.

    ~Will

    P.S. became friends with the :%s/JPG/jpg command - when I saved the images, the file extentions converted themselves to lowercase. God bless vi.

  • I think slashdot has discovered a mozilla bug.
    Everytime i click on the "out of legos" link, my
    Mozilla(1.0) crashes! ...Or maybe there is a new weapon against the /. effect!

  • Two heads are better.......than one (Score:4, Funny)

    by Tablizer ( 95088 ) on Wednesday July 03, 2002 @12:03AM (#3812298) Journal

    I would like to see this guy get together with the creater of this site:

    http://drew.corrupt.net/lp/series2.html

    The Kline Bottle would then never be looked at in the same light.

    (Warning: not for minors)
  • I wonder if Klein's bottle emerged waterproof. It will be a great vase for flowers if put to stand.
    I would like to have one, made of glass. Will look gorgeous, especially if made of colored glass.
  • Where does this guy get all of these lego blocks? It looks like he has all weird sizes too.

    Maybe he cheats and makes his own lego blocks... ;-)

  • Lego Mandelbrot Set, Anyone? (Score:3, Insightful)

    by Peahippo ( 539266 ) <peahippo@@@mail...com> on Wednesday July 03, 2002 @12:47AM (#3812400) Homepage
    I'm a firm believer in Legos * and am thoroughly convinced that they helped strongly in developing my inquisitive intellect. I still have my Legos from when I was 10.

    Look at 'em: they teach you to design, build, modify, and to have the patience for all of that. Legos are the best thing for the price that I can think of that can spur a young intellect. (Erector Sets were great for that too.) And if you get older and still play with them ... well, here's hoping that the world's first Lego Julia or Mandelbrot set will be made within our lifetimes. Lipson's surface models are just beautiful, so just imagine the beauty of a more sophisticated set.

    BTW, I am down on all this Lego model crap I see in the stores. Give kids a bucket of basic blocks and let them create ... that's the strength and appeal of Legos. However, I admit that the addition of gears makes the entire matter more challenging, perhaps for the 14+ age group.

    * Legos {tm} is the registered trademark of some silly corporation or something like that.

    • Re: (Score:1, Informative)

      by account_deleted ( 4530225 )
      Comment removed based on user account deletion
      • It amazes me that people who call Mnchen Munich can get all high an mighty when someone dares say "Legos".

        It's OK to change words--in all or some forms--when you import them into your language, to make them blend in better. There's absolutely nothing wrong with that and it's done all the time. Wouldn't it be simpler if Lego behaved like most other nouns? So why complicate matters?

    • I played with Lego gears since I was five years old, and I'm sure I'm not the only one.
  • ...doesn't his Klein bottle have multiple surfaces? Damn legos!

  • Not to be picky... (Score:3, Informative)

    by carnageonline ( 94229 ) on Wednesday July 03, 2002 @01:20AM (#3812479) Homepage
    Sorry, but technically a klein bottle is a four-dimensional figure (impossible to A) comprehend and B) create). Still looks cool!
    • Actually, a klein bottle is a 3d figure... it is an example of a figure which has no orientation (i.e. the inside is the same as the outside. Nothing impossible here, just a neat curiosity.
      • A kleinbottle is a 2d surface that cannot be represented in less than 4 dimensions without self-intersecting. It is basically a torrus, except that the tube goes through itself in 3d. A diagram of how to make one is:

        |-->--|
        ^' '' '^
        |--<--|

        Just line up the arrows and connect. For more information, check out mathworld.com.

  • It's LEGO!!!! (Score:1, Informative)

    by psyconaut ( 228947 )
    Why do people insist on saying Legos? The plural and singular of the word is: LEGO.

    I think it's the "sheeps" syndrome ;-)

    -psyconaut
  • One dimensional lego objects are cool, but can you make a machine out of them that keeps turning faster and faster?

    Oh, I'm sorry. I forgot that this post obeys the laws of thermodynamics!

  • As a kid, I couldn't even build the damn lego item on the box the legos came in! Most of the Lego creations I made were used to test fireworks' strengths.

    But, for those interested, here are some other cool Lego sites:

    Stegosaurus [henrylim.org]
    Lego Town [compuserve.com]
    Lego City [sparre.dk]
    Beethoven [henrylim.org]
    Queen Amidala [henrylim.org]
    Audrey Hepburn Wall [henrylim.org]
    Big Clock [ericharshbarger.org]
    Alice in Wonderland [ericharshbarger.org]

    • Wanna come over to my place and see my 14' lego stegosaurus?

      Yeah, there's a reason why my dining table is on the front lawn.

  • I once built a sphere out of lego. It was completely white and I still have it at home; I see it every day.

    I had no computer, not even a graphical calculator, so I had to calculate separately for each dot the distance to the center using and ordinary calculator and the pytogoras formula. The radius was 10 "units". Unfortunately, the unit brick in lego is not a cube. I think to ratio of base to height of these pieces is 5:6. So the sphere now looks more like an ellipsoid. Maybe I should photograph it and put it on the web.

  • Wow. Maybe it's the beer I just drank, but this is truly TRULY the coolest thing /. has shown in some time. Okay, maybe it's not strictly _news_, but WOW.
  • ...can he build a lego page counter than can keep up with the hits from /. ? :)
  • Lego is astonishingly easy to model in a 3d program.

    For inspiration, check http://ben.com/LEGO/ [ben.com] out

  • I'm sure I'm not the first to say it, but that's what it is.
    It always has been, it always will be, you can confirm this on their web site.
    It's like Sheep and Sheep - ok, NEVER call them "LEGOS" it grates people (whiners) like myself intensely.
    • Are you sure the plural is not LEGOES??? look at the word potato and the plural potatoes...

      Now don't have a hissy fit I like teasing whiners...
    • It's even less complicated than you make out. Lego is the name of a company. You don't pluralize it. You wouldn't say 'I have to reinstall several Microsofts this afternoon', would you? We call things Microsoft makes, 'Microsoft Applications' (if we're feeling generous). So, similarly, you wouldn't say you were going to build a moebius strip out of Legos. Lego bricks, Lego pieces, etc., yes, fine, but NOT Legos.
    • ...you'd hate for me to start my comment in the subject line, 'eh?
  • Anybody seen White Stripe's "Fell in Love With a Girl" video? Made entierly out of Lego's, using real Lego set, not CGI, as I thought first.
    You can see it here [mtv.com], along with some info of how it was done.

  • For people new to building and need a resources to buy their goodies, here [pitsco-legodacta.com] is a pretty good site. They have just about everything you would need (all different kinds of gears, axles, motor boxes, etc.). Everything you wish the main Lego site sold.
  • I found it very useful to have ideal surface renderings while contemplating the lego constructions.
    This site has nice rotatable images:

    http://mathworld.wolfram.com/topics/MinimalSurface s.html [wolfram.com]

    Nice job indeed!

    • It is not 'ideal surface', but 'minimal surface'. A minimal surface is a surface that has minimal area within certain constraints. Soap bubbles are examples of minimal surfaces. Floating in the air they ar not so very interesting. But when three or more bubbles stick together you get interesting membranes. Also using metal-wire frames and emmerging them in soap gives strange examples of minimal surfaces. FLT, not just any theorem.
  • The machine that turns itself off is so cool!! During math-colleges I was completely facinated by this idea and drew cartoon-like scenario pictures of it again and again, dreaming of building it. it probably appeals only to the more math-minded people.

    FLT, not just any theorem.
  • Let me know when he has made a model of Gabriel's Trumpet! Now, that would be something!
  • mmmmm yeah that's what I'm talkin bout.

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