Allegorithmic's method may be near impossible for this, but I couldn't help myself and tried recreating one of the classic methods (the left one of your gifs).

As I mentioned, this requires quite a few samples to do.
Filling this island took 2048 pixel processors for a total of 12288 samples *per pixel*.
Filling this star requires twice as many. It would take less at lower resolutions though.

This could be optimized a bit though.
I could hopefully somehow take a lot more samples per pixel processor, which would speed it up a little and maybe add some "cheaty" functionality to jump x amount of pixels per sample. Or maybe by starting at a very low resolution and turn it up every x number of steps.
Filling all islands with different colors is probably possible without needing more samples, but fancy stuff like gradients is a no-go.
Maybe I can find some time here and there over the next couple of days/weeks.