I made up my own theory about raising a hypercomplex number to an arbitrary power in 3D space, plugged the formula into the volumeRender SDK demo at 512x512x512 voxels and got this. Pretty cool, uh? Not your usual z^2+c Mandelbrot. More like a distant cousin (at least when looked at from the other side).
From the first angle this looks almost like your usual mandelbrot.
But watch what happens when I rotate.
Oh wow, this was unexpected.