One thing I've often wanted to do, but didn't have the time to, was to take Turing Drawings: https://github.com/maximecb/Turing-Drawings ( faster asm.js variant here: https://github.com/darius/Turing-Drawings ), which runs a random Turing machine to generate abstract art and put the machine description in the image itself, so it could self-modify.

The links you gave are fascinating! Believe it or not, I have done something like that, too: http://imgur.com/gallery/sRUrI

To be fair, that seems to require turning off in the middle of a save. Not entirely by the rules of the game.