This is beautiful. I had thought about how can small programs produce complex outputs, and why most strings are incompressible, and now I know that for any program with size N, there can be only 2**n strings that can be compressed…. I knew it was naive to assume no one had thought that before, and here’s all of it!
Complex output from seemingly simple systems is at the center of Stephen Wolfram’s work developing what he calls “a new kind of science,” which is also the title of his book. If you’re into this kind of stuff, I highly suggest checking out his talks and writings, such as this talk from 2008 about complexity and computation, or this article about a possible path to a unified theory of physics.