The familiar Mandelbrot Set is actually just one 2D slice out of the larager 4D Mandelbrot/Julia Set fractal. This object is generated as successive slices beginning with the Mandelbrot slice in which the initial Z values are initialized to 0, and then successive slices allow the initial Z-imaginary component to vary. You can see the outline of the Mandelbrot shape in the cross-section. Gluing two of these together makes one of the two such canonical 3D objects, the other being the one where the imaginary value is held to 0 and the real value varies.
Black is the ideal color since that is the traditional color for renderings of points in the Mandelbrot Set.