Mandelbulb: The Unravelling of the Real 3D Mandelbrot Fractal
There are some astonishing images at this link, along with a little math, and a dab of graphics know how. The discussion brings in some aesthetic issues, like focus and zoom, plus lighting and coloration to demonstrate how to express the object to its best potential. If you don't care about all that, you'll still be hooked by the pictures.
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