The Mandelbulb is a 3-dimensional analog of the Mandelbrot set, created by Daniel White and Paul Nylander. Since the 2d Mandelbrot set exists in the space of complex numbers (a + bi, where i is the square root of 2), the 3d Mandelbrot must occupy a space of “hypercomplex” numbers.

The hypercomplex algebra is complicated, but the important thing is that the Mandelbulb uses the map z -> z^n + c    (different values of n generate different Mandelbulbs). The most well-known Mandelbulb seems to be the one generated by n=8:

Just like the Mandelbrot set, the Mandelbulb displays “pseudo-fractal” morphology. There don’t appear to be any exact repetitions, but there are bulbs upon bulbs upon bulbs……. Additionally, we cannot discern our level of zoom just by looking at the level of detail.

Here is a video of a zoom into the Mandelbulb:

For more information, see and

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