"Mandelbulb," a 3D Mandlebrot Construct, Discovered

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."

Comments

Looks like a big sea slug.

[Ethanol-fueled]

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?

Re:Actually, the Mandelbrot set is already 4D

[jhesse]

This.

You can find a picture of a "4-D" Mandlebrot set in a mid/late 80's issue of Scientific American.
I was generating pictures of this on a 286 pc. (with EGA graphics) 15 years ago, and the pictures
in TFA of z^2 look *nothing* like that did.

Re:Actually, the Mandelbrot set is already 4D

[Eudial]

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.

Animated quaternion

[_bernie]

The common Mandelbrot set is really a 2-dimensional slice of a 4-dimensional object identified by both the combination of the complex numbers Z0 and C in the canonical Zn+1 = Zn^2 + C. The mandelbrot set lives in the plane where Z0 = 0 + 0i, while the Julia sets live on infinitely-many-squared orthogonal planes in the remaining two dimensions, each one intersecting Mandelbrot's plane in a single point of complex coordinates C.

Visualizing this hyperspace monster was made easy by POV-Ray. It took my computer two week of computation to render 80 seconds of animated 3D slices of a the quaternion. Check out the scene source.

/me looks forward for a real-time Julia4D explorer.

Re:Actually, the Mandelbrot set is already 4D

[fractoid]

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".