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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."

17 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 Eudial · · Score: 5, Interesting

      While not a pure mandelbrot, but a buddhabrot rendering: For the curious, here's a nice 2D projection of such a (rotating) 4D fractal I whipped up a while back.

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      GAAH! MY PRINTER IS ON FIRE!!! PUT IT OUT! PUT IT OUT!
    2. Re:Actually, the Mandelbrot set is already 4D by Garble+Snarky · · Score: 5, Insightful

      I was following the fractalforums thread for a while, and IIRC that is what a lot of the discussion focused on - "how can we define the squaring operation in 3D such that the Mandelbrot iterative equation gives us something like our vague notion of what we want the Mandelbulb to look like?"

      Site is down, but I got an email notification from fractalforums a few days ago, and they had some incredible results. The pursuit is at least as much aesthetic as it is mathematical, and in that respect they've succeeded marvelously.

    3. Re:Actually, the Mandelbrot set is already 4D by maxwell+demon · · Score: 5, Insightful

      People who say they see 3-D crack me up, since the back of the eye is a 2-D surface.

      But most people have two eyes, and the parallax between them gives the third dimension.

      --
      The Tao of math: The numbers you can count are not the real numbers.
    4. Re:Actually, the Mandelbrot set is already 4D by fractoid · · Score: 5, Interesting

      This post needs more +insightful. What a lot of people are missing by getting wound up in the maths is that it is an artistic endeavour. Their definition of "a mandelbrot" (and yes, this broken terminology bugs the pedant in me beyond belief) is nothing to do with z^2+c, and everything to do with "a pretty looking blobby thing that maintains an aesthetically pleasing and visually interesting level of surface detail at all magnifications".

      --
      Rampant carbon sequestration destroyed the Dinosaurs' tropical paradise. I'm here to help repair the damage.
  2. Ice Cream From Uranus? by Anonymous Coward · · Score: 5, Funny

    That ruined it for me.

    1. Re:Ice Cream From Uranus? by SeNtM · · Score: 5, Funny

      Professor: "I'm sorry, Fry, but astronomers renamed Uranus in 2620 to end that stupid joke once and for all."
      Fry: "Oh. What's it called now?"
      Professor: "Urrectum. Here, let me locate it for you."

      --
      "There ought to be limits to freedom." -George W. Bush
  3. That thing looks like all of my nightmares. by Anonymous Coward · · Score: 5, Funny

    You could put it in a horror movie and make it pulsate.

  4. Looks like a big sea slug. by Ethanol-fueled · · Score: 5, Interesting

    I wonder if we'll ever reach the point where we will be able to define, with equations and rules, a sea slug using the principles of cellular automata?

  5. Re:Not a "true" 3D Mandelbrot by Anonymous Coward · · Score: 5, Funny

    You must be new here.

  6. 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.
  7. A sad day indeed... by symbolset · · Score: 5, Insightful

    If that's the case, it's been a sad day since at least 1984. These things teach us interesting things about numbers and are interesting in and of themselves. As a way of making math more visually beautiful they also serve to draw the interest of youth to a field ordinarily seen as dry and boring.

    --
    Help stamp out iliturcy.
  8. 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)

  9. Re:All I see is a big white rectangle by MobileTatsu-NJG · · Score: 5, Funny

    With a message saying Page cannot be displayed. Not that impressive.

    Did you try zooming in?

    --

    "I like to lick butts!" by MobileTatsu-NJG (#32700246) (Score:5, Informative)

  10. a great leap forward by circletimessquare · · Score: 5, Funny

    for scientific screensaverology

    --
    intellectual property law is philosophically incoherent. it is your moral duty to ignore it or sabotage it
  11. 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.
  12. Re:Elder feuds reignited? by Bill+Currie · · Score: 5, Funny

    *Burp*

    And tasty they were, too.

    --

    Bill - aka taniwha
    --
    Leave others their otherness. -- Aratak