[crazygringo]

In practice, the Mandelbulb is usually only computed to a few iterations (e.g. 20) in order to maintain smooth surfaces and prevent a lot of surfaces from dissolving into ~disconnected "froth".

So deep zooms and deep iterations aren't really done for it.

Also, it's generally rendered using signed distance functions which is a little bit more complicated. I haven't looked at the equations though to figure out if perturbation theory is easy to apply -- I'm guessing it would be, as the general principle would seem to apply.