The comments on Vimeo indicate that the creator is aware of this and is (or rather was, a year ago when it was posted) working on something more interesting. Here's a more recent one by the same person, which I preferred: http://vimeo.com/1973524 and another, which traverses more interesting bits of the set than either but isn't of such high video quality: http://vimeo.com/9522366
That and a lot of time zooming toward what I think are Misiurewicz points--if memory serves me, places on the boundary of the set where multiple "branches" meet, and tend to have very strong self-similarity along the branches and detail shrinking infinitely as the branch point is approached.
a) What is the speed of light in the mandelbrot set? What zoom level do you designate to be 1m?
b) The 'speed' the camera is traveling at is hugely variable. It's basically slowing down by an order of magnitude every constant window of time. So if the final image is 1m wide, you're travelling 10^n's of universes every second at the start. The above sentence doesn't come close to doing this idea justice.
Update: the sentence is from the original at http://vimeo.com/1908224
I went over the video a second time to see how often the camera 'steers'. The entire second half drops pretty much straight down a radially symmetrical 'well'. There's 2 obvious changes in bearing between 2 and 5 minutes. In the first 2 minutes it's harder to keep count because much of the time there's no radial symmetry. I suspect the bearing is changing almost constantly.
Summary: the video was made by choosing a point about 2 minutes worth of zoom in, and then pretty much dropping straight down, except for a couple of tacks. Whoever did this was probably trying to maximize the diversity of views; at any point in the video a different tack may have ended up back at something like the starting point much sooner. It's mind-blowing to contemplate.
So, it's like the way adding integers is O(1), right? Sure... as long as your integers are always 32 or 64-bit and you don't mind a bit of light truncation. In general it's higher than that.
So you're doing more iterations, with higher-precision numbers, as you zoom closer in.
EDIT: Added "pixel on the screen".
Fractals are in episode 6 from ~8 minutes onward:
And regarding "prime-ness", I mean I didn't notice any patterns with 7, 11, or 13 features -- that sort of thing.
I suppose the prominence of powers of two has something to do with "period doubling" in chaos theory, I don't know.
And that color-cycling one is... I dunno, hallucination / head-trip inducing o_O I can't tell if I want to keep watching or not. It's kinda too much, but it's pretty...
The ending is not to be missed.