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"Mandelbulb," a 3D Mandlebrot Construct, Discovered

Posted by kdawson on from the to-boldly-go dept.

symbolset writes "Many know the beauty and complexity of the Mandelbrot set. For some years now a few enterprising mathematicians / rendering fiends have been seeking a true 3D Mandelbrot set. A month ago a solution was found, and it is awesome to behold."

14 of 255 comments (clear)

  1. Actually, the Mandelbrot set is already 4D by maxwell+demon · · Score: 5, Informative

    While the Mandelbrot set as usually defined is 2D, each point has an associated Julia set, where instead of the additive constant, the starting point is varied (the original Mandelbrot set always uses zero as starting point). Together, they give a 4-dimensional set, where two dimensions are given by the starting point (zr, zi), and the other two by the additive constant (cr, ci). The original Mandelbrot set is a cut through this 4D set at the plane zr=zi=0, while the Julia sets are cuts orthogonal to theat, at planes with constant cr and ci.

    --
    The Tao of math: The numbers you can count are not the real numbers.
    1. Re:Actually, the Mandelbrot set is already 4D by maxwell+demon · · Score: 2, Informative

      Ever tried the "Magic Eye" pictures? There's exactly zero visual cues. Unless you manage to look at the image so that the left-eye and right-eye see it with a certain displacement (so different parts of the picture now match), you see not a single trace of the 3D figure hidden in it). The only depth information that is there is the displacement.

      --
      The Tao of math: The numbers you can count are not the real numbers.
    2. Re:Actually, the Mandelbrot set is already 4D by Eudial · · Score: 2, Informative

      Archive.org offers the full .avi file for download (the AVI version is about 4000 times more awesome than the flash version), and it's in public domain, so you are perfectly within your rights to go do it yourself.

      --
      GAAH! MY PRINTER IS ON FIRE!!! PUT IT OUT! PUT IT OUT!
    3. Re:Actually, the Mandelbrot set is already 4D by Anonymous Coward · · Score: 1, Informative

      It's been proven that there is no normed division algebra over R (real numbers) which has dimension 3 (over R). More specifically, the only normed division algebras over R are R itself, complex numbers, quaternions, and octonions. So, in that meaning of sensible it can't be done.

    4. Re:Actually, the Mandelbrot set is already 4D by Anonymous Coward · · Score: 1, Informative

      It's a "Me too!", but for Slashdot. It means "I wanted to say exactly the same, but someone else was first. Rather than saying nothing, I will clutter up the discussion".

      The GP (grandparent) did add a bit of his / her own, so it wasn't as bad in this case.

  2. Not a "true" 3D Mandelbrot by HEbGb · · Score: 4, Informative

    It's definitely nifty, the pictures are beautiful, and the creator deserves praise, but the author himself says it's probably not a "true" 3D Mandelbrot:

    http://www.skytopia.com/project/fractal/2mandelbulb.html#epilogue

    As exquisite as the detail is in our discovery, there's good reason to believe that it isn't the real McCoy. ... ...
    Evidence it's not the holy grail? Well, the most obvious is that the standard quadratic version isn't anything special. Only higher powers (around after 3-5) seem to capture the detail that one might expect. The original 2D Mandelbrot has organic detail even in the standard power/order 2 version. Even power 8 in the 3D Mandelbulb has smeared 'whipped cream' sections, which are nice in a way as they provide contrast to the more detailed parts, but again, they wouldn't compare to the variety one might expect from a 3D version of Seahorse valley.

    So, Slashdot, I know this is asking a lot, but can you PLEASE at least read the article before posting? Thanks.

    1. Re:Not a "true" 3D Mandelbrot by symbolset · · Score: 3, Informative

      There is a subtle difference between "a solution" and "the solution".

      But yeah, I was selling it a bit because the pictures are so lovely.

      --
      Help stamp out iliturcy.
    2. Re:Not a "true" 3D Mandelbrot by Sebilrazen · · Score: 2, Informative

      Looking at their UID I'd say they were here when here was new.

      --
      "There are no facts, only interpretations." --Friedrich Nietzsche.
  3. Zooming by Spy+Hunter · · Score: 4, Informative

    Here's a 7500x7500 (56 megapixel) image of the fractal: http://seadragon.com/view/fnr.

    --
    main(c,r){for(r=32;r;) printf(++c>31?c=!r--,"\n":c<r?" ":~c&r?" `":" #");}
  4. Slashdotted by Kaladis+Nefarian · · Score: 5, Informative

    Seems to be slashdotted, cached version: http://www.skytopia.com.nyud.net:8090/project/fractal/mandelbulb.html

    --
    * Several monkeys are here, playing banjos and wearing small hats.
  5. w00t by lycium · · Score: 5, Informative

    cool, nice to see my images linked on slashdot :) hopefully we'll have some gpu-accelerated results to show you all soon (and for those with opencl supporting cards, executables).

    btw interested parties might like to check out my 3840x2400 resolution render of the 7th degree version here: http://lyc.deviantart.com/art/siebenfach-139038934 (it's buried deep in the thread, and fractalforums is creeking a bit)

  6. Fraqtive by nephridium · · Score: 5, Informative

    A very nice open source app, available through the Ubuntu/Debian repositories. The author's page even got a windows version.

    It supports multi-core CPUs, i.e. if you really want to tax each of your CPU's core to the limit, just use the app to browse through the mandelbrot set. It also supports a 3D extrapolation of the 2D set (OpenGL and software).

    Strangely enough it doesn't seem all that popular, as the forum doesn't seem all that populated..

    --


    And when you gaze long enough into the code, the code will also gaze into you.
  7. Re:Looks like a big sea slug. by scheme · · Score: 3, Informative

    It's all chemistry, physics and math.

    Has anyone actually done this? With even a ''simple'' organism ( yes, those are air-quotes ), like a paramecium? It sounds easy in theory, but I bet when we actually get down to it, there'll be a few speedbumps and unexpected obstacles in the way.

    Things are not even close. Look at vcell to see what's close to the state of the art in cell simulation. Right now, it's a matter of trying to get a few reactions and cell compartments working correctly. I don't think anyone has even come close to modeling any type of complete cell.

    --
    "When you sit with a nice girl for two hours, it seems like two minutes. When you sit on a hot stove for two minutes, it
  8. In nature - I give you, Brassica oleracea! by zooblethorpe · · Score: 3, Informative

    These particular fractals remind me of things I hope never to see in nature.

    Some of it, at least, has already happened: see this fine example of Brassica oleracea, for instance.

    Then again, you might have been referring to some of the fractal images that call to mind the work of H. R. Giger... < shiver >.

    Cheers,

    --
    "What in the name of Fats Waller is that?"
    "A four-foot prune."