Mandelbulb: 3D Mandelbrot

The Mandelbulb is an attempt to extrude the classic Mandelbrot Set fractal into three dimensions. I'm not enough of a mathematician to say whether it accomplishes this feat, but it is utterly arresting.

Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal: (via /.)



  1. looks like a scene from Tim Burton’s Sleepy Hollow…. very pretty, yet creepy at the same time (probably mostly due to it being dark and grey?)

  2. The effect is stunning. There have been other not-quite-3D/2.5D style attempts at this sort of thing in the past, beautiful in their own right, but the impact of the Mandelbulb visuals are amazing.

  3. Those 3D models are wicked awesome. I would love to plug the info into a 3D printer, and get some awesome sculptures out of it.

  4. wasnt the mandelbrot set and other fractal sets created to mathematically describe the natural world? the natural 3d world? so if you want to see a fractal set in 3d just look out yer window at a tree or a flower or an acorn.

    fake edit: not to minimize the work on the madlebulb, its stunning

  5. The beauty!

    Fractals are now being used to generate starting grids for neural networks giving more realistic results. This mandelbulb looks like the starting point for something beautiful.

  6. @cymk
    Yeah, but I would want it BIGGER :)

    3D printers have that pesky size limitation, unless you do it part by part (which would be pretty cool)

  7. @arikol

    I was thinking something on the size of the machines used by car manufacturers to make the life sized models out of foam and clay.

  8. I would think the whole “infinite” thing would be more problematic than size limitation, if you’re making physical models.

  9. I feel somewhat nauseated at these pictures. There’s something… coldly organic in them, like an unfinished blueprint for a living thing.

  10. Reminds me a lot of Gaudi’s work, specifically Sagrada Familia. Would like to see this implemented into some sort of architectural nightmare that really couldn’t ever be finished. In any case, very cool stuff.

    1. “some sort of architectural nightmare that really couldn’t ever be finished”

      Sounds like a certain notable hole in the ground in lower Manhattan. And/or a Borges story.

  11. @Moriarty
    Nah, you could set a limit to the ‘level’ of the rendering and output a fairly detailed model.

    Uh.. wait a sec, was that a rhetorical question?

  12. I’m with lysdexia@6. The Laundry called. They’d rather we stopped summoning eldritch entities from beyond our universe with those arcane computations…

  13. Weird how I’m getting kind of a fear/disgust reaction to some of them. Like I’m looking at some kind of horrible fungus or mold and am breathing in toxic spores that are going to sprout out of my body, just by looking at these images.

  14. Ooooooohhhh…… Nerdgasm! Since the first time I ever wrote code to construct the Mandelbrot set I’ve dreamed of it in 3D.

    Note to self: follow more dreams

  15. Wow, it’s funny that how these images invoke in me (and other commenters) a strange feeling of fear and repulsion. The resemblence to fungi is a possible reason for this…but I don’t know…maybe there’s some polar opposite to the golden ratio that we’re picking up on.

  16. Oh my goodness! I tried doing 3d depth Mandelbrots in the nineties. Not like this though, much less the-amazing-rolling-landscapey-shit-they’ve-achieved-here, but similar enough for me to feel a small pang in my heart. It’s amazing stuff, I must follow their progress. Maybe even relook into the stuff I was trying.

    1. Yeah, it’s making me want to start the whole fractal exploration thing again. I taught my stepson how to generate the set (trying to get him into math, which he used to hate) then passed him a copy of Turbulent Mirror.

  17. Very nice work Cow, I can totally see the depth in it. Similar to some of the ones I tried to revisualize in the third dimension :)

  18. WOW.. i love fractals since i’ve seen some of them in the late 80’s.
    i don’t understand the maths behind them but this is absolutely fascinating. these 3D fractals are the most stunning graphics i’ve ever seen.
    it’s like a nightmare of h.r. giger…not a nightmare for the fans..
    simply great
    in german: hammerhart

  19. z_(n+1) = z_n^2 + c | z_0 = c (2D classic)
    pow 2: z = z^2+c i*j=-j, i*j=i

    pow 3: (without transform)
    |[{x,y,z)^n]| = (x^2+y^2+z^2)^n/2
    with transform: (x,y,z)^2 = x^2-y^2-z^2-2yz,2xy,2xz)
    (x,y,z)^2 = x^2-y^2-z^2+2yz,2xy,2xz)

    pow 8, which dspwhite (or Michael White) showed the zoomed transform:
    phi = atan2( pow(a.x*a.x + a.y*a.y, 0.5) , a.z)
    n.x = r * cos(phi) * cos(theta)
    n.y = r * cos(phi) * sin(theta)
    n.z = r * sin(phi)

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