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.