I can't remember why I put this 2009 book on my get-at-library list. Nevertheless, I did, and I did. And it's pretty good! It's roughly at the smart-STEM-undergrad level. The author, Melanie Mitchell, is a CS professor at Portland State, and an "External Professor" at the Santa Fe Institute, which is "dedicated to the study of complex adaptive systems."
To call the book wide-ranging would be an understatement. Because (to be flippant) pretty much any scientific field can get complex, if you want to go that way. Specifically, real-world systems have "emergent" properties, neither predictable nor (even) explainable by analysis of their simpler constituent parts.
So here's a partial sampling of what shows up: logistic maps; gene expression; insect colonies; statistical thermodynamics; cellular automata; networks; evolution; genetic algorithms; self-reproducing computer programs; analogy-generation (Mitchell's own research contribution). All clearly (and sometimes humorously) described, and she's not above showing you some math.
I had a "Wow" moment when Mitchell described the discovery of the Feigenbaum Constant; its value (4.6692016…) shows up in some pretty conceptually-simple math underpinning chaotic systems and deserves a spot along (say) π or e. Or maybe Euler's constant.
Mitchell also gives space to the critics of complex systems research. Are there really underlying principles governing the general behavior of complexity? Sort of a unified field theory? Mitchell admits that they aren't there yet. Amusingly, she points to a Scientific American article debunking complexity, in which she was quoted, she says unfairly. Given Scientific American's record on other issues, I'm inclined to take her side.