I'm curious why no source ever seems to mention that the Mandelbrot set and the Julia sets can be regarded as perpendicular cross-sections of a single 4 dimensional fractal. Its four dimensions are real c, imaginary c, real z, and imaginary z. The Mandelbrot set is the cross-section where the two z coordinates are both zero. The Julia sets are cross-sections where the two c coordinates are constants.
I'm working on a program which will let me view arbitrary cross- sections of the thing. I'm attempting to visualize what the whole thing looks like. I also plan to try and measure its 4-volume.