Video from still images - Zooming
Interesting question. First, here's a question for you: can your supercomputer actually calculate and render, in real time, an animated zoom on images so complex?

My guess (only a guess) is that it will need more than 1/30 sec. to complete each frame (let's assume 30 frames per second as a minimal frame rate in which to achieve a smooth zoom). If that's the case then you just need to spit out x number of images (bitmaps) that can be played back later, at 30 f.p.s., by any non-super computer. 

A zoom is just a scale change. Assuming that you don't have in mind a particular rate of change in scale -- in other words, that you don't need to get to a particular scale in a particular time -- try 1% of scale-increase per frame (I'll check this and post an update if you can do much better).  

Satisfactory zooming will also involve easing at the head and tail of the zoom. If you need an easing algorithm, just ask. It probably won't be in the language you're using but you'll be able to figure it out.



UPDATE -- I just read something about Blue Gene. Maybe it can do 800x600 Mandlebrodt images @ 30 f.p.s.!  But the same rate-of-change applies -- smoothness is a human perception thing.