Try the Fractal eXtreme demo.
That video is pretty dull compared to what really exists "in there" - way too much zooming into "infinity pits".
It's the points of bifurcation that lead to the most interesting patterns (you don't need to know math, your eyes will figure that one out).
The colormap rate scaling is the bigger challenge - balancing iteration count against what's actually needed for the rendering......
This all sounds complex, but it's really pretty easy if you have it in front of you.....
