Mandelbulb: 3D Mandelbrot


42 Responses to “Mandelbulb: 3D Mandelbrot”

  1. IWood says:

    I want to meld this concept with expanded polystyrene foam construction and build a house. Then I’ll commission H.R. Giger to design furniture for the space.

    Then I’ll sit inside my new home and go mad.

  2. Anonymous says:

    It’s Romanesco Broccoli!

  3. Thomas says:

    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)

  4. JamesPadraicR says:

    I first saw this on Rudy Rucker’s blog a few days ago. At first I thought it was a large wasp nest.

  5. Anonymous says:

    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

  6. Anonymous says:

    i saw this when i smoked 35x salvia.

  7. Yhancik says:

    That reminded me of Torsten Fleisch’s Gestalt :

    It’s a bit like what nanuq what looking for ;)

  8. misterjuju says:

    Ice cream from neptune? or.. FRACTAL PENIS?! (penises?? Peni? meHHH)

  9. Anonymous says:

    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?)

  10. Anonymous says:

    Norbert Weiner channels broccoli.

  11. benher says:

    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.

  12. daev says:

    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

  13. Gloria says:

    I’m just slack-jawed.

  14. Anonymous says:

    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.

  15. cymk says:

    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.

  16. Anonymous says:

    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

  17. arikol says:

    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.

  18. arikol says:

    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)

  19. Cowicide says:

    Please Gawd someone convert my fractal to 3D, I’ll give you all the equations for it… It was born to be 3D…

  20. Anonymous says:

    I expect to see this in Guillermo del Toro’s next film. Oddly elegiac.

  21. lysdexia says:

    Every time I look at it, I keep expecting to see Cthulhu poking his head out.

  22. cymk says:


    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.

  23. Anonymous says:

    Grandma likes to knit.

  24. Moriarty says:

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

  25. Takashi Omoto says:

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

  26. CastanhasDoPara says:

    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.

  27. nanuq says:

    Is there a video anywhere on the site? A video with sound effects would add to the experience.

  28. Enormo says:

    This work has been commended as being very vaginal.

  29. Anonymous says:

    To see 5 huge mandelbulb, mandelbox :

  30. benher says:

    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?

  31. Kaden says:

    Looks like X-Treem Crocheting.

  32. AceJohnny says:

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

  33. Crashproof says:

    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.

  34. arkizzle / Moderator says:

    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.

    • daev says:

      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.

  35. arkizzle / Moderator says:

    Good job Daev, there’s room for generations here :)

  36. Anonymous says:

    If you want to see a 132 Megapixels image, take a look here,, and click on the image to see it with OpenLayers.

  37. arkizzle / Moderator says:

    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 :)

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