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 /.)

Previously:

I write books. My latest is a YA science fiction novel called Homeland (it's the sequel to Little Brother). More books: Rapture of the Nerds (a novel, with Charlie Stross); With a Little Help (short stories); and The Great Big Beautiful Tomorrow (novella and nonfic). I speak all over the place and I tweet and tumble, too.

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IWood

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.
Anonymous

It’s Romanesco Broccoli!
http://silencefreedom.deviantart.com/ Thomas

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)
JamesPadraicR

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

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
ralf-j
Anonymous

i saw this when i smoked 35x salvia.
Yhancik

That reminded me of Torsten Fleisch’s Gestalt : http://www.fleischfilm.com/html/gestalt.htm

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

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

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?)
Anonymous

Norbert Weiner channels broccoli.
benher

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.
daev

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
Gloria

I’m just slack-jawed.
Anonymous

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.
cymk

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.
Anonymous

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
arikol

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.
arikol

@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)
Cowicide

Please Gawd someone convert my fractal to 3D, I’ll give you all the equations for it… It was born to be 3D… http://www.flickr.com/photos/49403380@N00/2437476071/
Anonymous

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

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

@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.
Anonymous

Grandma likes to knit.
Moriarty

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

I feel somewhat nauseated at these pictures. There’s something… coldly organic in them, like an unfinished blueprint for a living thing.
- JonStewartMill
  
  I smoked salvia divinorum once, and saw something like these images. Once was enough.
CastanhasDoPara

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.
- Gloria
  
  @10: Great thought. Love it.
- Moriarty
  
  “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.
nanuq

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

This work has been commended as being very vaginal.
- cymk
  
  Damn it, now I can’t get that Maude Lebowski monologue about her art out of my head.
Anonymous

To see 5 huge mandelbulb, mandelbox :

http://renaud.warnotte.be/Projects/Mandelbulb/Albums/
benher

@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?
Kaden

Looks like X-Treem Crocheting.
AceJohnny

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

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.
arkizzle / Moderator

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
  
  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.
arkizzle / Moderator

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

If you want to see a 132 Megapixels image, take a look here, http://renaud.warnotte.be/index.php/fr/news/40-categorynews/130-mandelbulb-high-resolution-image-132-megapixels, and click on the image to see it with OpenLayers.
arkizzle / Moderator

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 :)