Fractal
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.
clipped from en.wikipedia.orgMandelbrot setThe 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.
clipped from www.youtube.comExterminate - Mandelbrot Fractal Zoom Music Video
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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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.comMandelbulb zoom
A zoom into the 3D mandelbulb (split in half), with full light sourcing. Enjoy.
clipped from www.youtube.com3D 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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Sources:
- Fractal - Wikipedia, the free encyclopedia
- Mandelbrot set - Wikipedia, the free encyclopedia
- YouTube - Exterminate - Mandelbrot Fractal Zoom Music Video
- Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal
- The Unravelling of the Real 3D Mandelbrot Fractal
- YouTube - mandelbulb zoom
- YouTube - 3D Mandelbulb mountain cross sections
