Something like Turing's busy beaver problem. You can get huge amounts of complexity from very little initial "state" information. https://en.wikipedia.org/wiki/Busy_Beaver_game The pigeonhole principle means there are only a limited number of patterns that you can generate from a few bits. http://atlas.wolfram.com/01/01/ But the complexity of the output means you can often find something useful if you can pick a subset of the output. E.g. http://www.dr-mikes-math-games-for-kids.com/your-name-in-pi....

Of course, describing that subset is itself using bits

https://github.com/philipl/pifs