Reaching the specified limit: The Recursive Universe: Cosmic Complexity and the Limits of Scientific Knowledge by William Poundstone.

This is another book which comes at things from lots of angles - it talks about Conway's Life, Maxwell's Demon (in several variations), self-reproduction ... it clears up a number of apparent paradoxes in an engaging and understandable way and explains a lot of really cool concepts on the way to understanding how patterns can arise from noise.