Apologies in advance, but this isn't really a photoshop question. Rather, I'm trying to come up with something that is convincing but exploits the compression and features of the gif format as best as possible to produce the smallest possible file for the animation.
Some constraints:
Also acceptable: an apng that complies with the above constraints. Possibly even mpeg, if you can come up with that (I'm ignorant of how the DCT does its magic).
Ideally I could get something down in the 250kbyte range, but I'd settle for anything significantly smaller than the 9 meg monstrosity I cooked up last week.
Oh, and one last thing: obviously I don't expect anyone to supply the graphic for me. I'm just looking for some trick(s) that will let me get there myself eventually.
This is a very interesting question.
Static (random noise) by its nature is actually highly incompressible. Information theory says that true noise is basically incompressible, and the more patterns something contains the more compressible it becomes (to the point of a solid line of 1's or 0's being perfectly compressible.
The ideal would be to create a true noise generator (just random numbers), but that doesn't help within the constraints of your problem.
The best thing I can think of is storing a number of small tiles of static and displaying them in staggered fashion to prevent the eye catching on to any patterns. Aside from that, you won't have much luck compressing this beyond 256 x 192 x 20 / 2 or about 500 kilobytes ( assuming 20 frames with resolution of 256 x 192, using 4 bit color depth ).
Simply encoding your animated gif in 16 color mode should get you to that point.
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