> Maybe I've misspoken somewhere.
>
> Figuring out what color to make one pixel near the end of the video
> doesn't take more iterations than figuring out what color to make one
> pixel near the start of the video?

To be absolutely technically correct, computing pixels at a higher 
magnification does not /necessarily/ require more iterations. However, 
if the part you're magnifying is one of the "interesting" bits (i.e., 
not a screenful of flat colour) then yes, yes it does take more iterations.

> I don't see how this works out, tho. If you have 256 colors, you (could)
> do 256 iterations for each pixel, regardless of the mapping of the
> cartesian plane to the screen, yes?

If you only do 256 iterations, then after a very modest zoom (30x or 
so), you won't see any additional detail.

(I presume you meant "up to" 256 iterations, since the pixel's colour 
indicates the exact number of iterations performed - or in this case, 
the least significant 8 bits of the count, anyway...)

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