For something in a similar vein, but perhaps more approachable, check out The Computational Beauty of Nature (http://www.amazon.com/The-Computational-Beauty-Nature-Explor...).
I am going to go buy a copy now just, well, because I can.
have you read that book and would you recommend it over "The Fractal Geometry of Nature by Benoit Mandelbrot (1982) [1]?
I'm asking because I bought the latter and would like to know if this book provides more recent information on the topic.
Thank you.
--
[1] http://www.amazon.com/Fractal-Geometry-Nature-Benoit-Mandelb...
I don't know what sort of depth you're looking for, but I'd call CBoN a "medium"-depth book on the subjects involved. It's possible to read it like a pop-science book and still appreciate it, but you can actually sit down with pencil and paper (or write some code) and gain a pretty good level of insight. You're not going to necessarily gain a complete understanding of all the underlying math, though, just by reading this book.
Anyway, it's a pretty darn good use of $40, IMO. Buy it!