The Mandelbulb a 3D Mandelbrot Set

clipped from en.wikipedia.org
A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity.

The Mandelbrot set is a famous example of a fractal

clipped from en.wikipedia.org
Mandelbrot set
The Mandelbrot set is self-similar under magnification [...]
Zoom animation
Regardless of the extent to which one zooms in on a Mandelbrot set, there is always additional detail to see.
Mandelbrot color zoom.gif
clipped from www.youtube.com

Exterminate - Mandelbrot Fractal Zoom Music Video

clipped from www.skytopia.com

The Real 3D Mandelbulb

It's found by following a relatively simple math formula. But in the end, it's still only 2D and flat - there's no depth, shadows, perspective, or light sourcing. What we have featured in this article is a potential 3D version of the same fractal.

Resulting renders

But it wasn't until I incorporated proper shadowing that the subtleties of this incredible object became apparent. For the renders below and exploration afterwards,

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clipped from www.skytopia.com
Further exploration of the 3D Mandelbulb

What does it look like on the inside?

Any interesting analogues to the 2D Mandelbrot set?

A 3D Mandelbrot stalk (a deep zoom inside the Bulb)

A 2D Mandelbrot stalk

A 3D Mandelbulb spiral (found at a deeper zoom inside the "Ice Cream from Uranus" picture). Click to enlarge, and see this page of the thread for how it was found.

A 2D Mandelbrot spiral

Are gorgeous flyovers and parallax zooms now possible?

clipped from www.youtube.com

Mandelbulb zoom

A zoom into the 3D mandelbulb (split in half), with full light sourcing. Enjoy.

clipped from www.youtube.com

3D Mandelbulb mountain cross sections

Over 1000 cross sections of a zoomed in section from the 3D Mandelbulb. Observe the absurdly ornate detail within. This took around a couple of days to render.

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  1. Fractal - Wikipedia, the free encyclopedia
  2. Mandelbrot set - Wikipedia, the free encyclopedia
  3. YouTube - Exterminate - Mandelbrot Fractal Zoom Music Video
  4. Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal
  5. The Unravelling of the Real 3D Mandelbrot Fractal
  6. YouTube - mandelbulb zoom
  7. YouTube - 3D Mandelbulb mountain cross sections
  1. Welcome - True 3D mandelbrot type fractal
  2. Patterns of Visual Math - Mandelbrot Set
  3. Skytopia - Mystery of the Real 3D Mandelbrot Fractal