The sad thing is that I lived so much of life without ever coming across fractals.
I have not learned as much new in a single book ever. From the coastline length concept to Mandlebrot Sets, Feibengaum constants to Lorenz attractors, Julia sets and Cantor sets, the world of non-linear mathematics that is even at the fringe of linear mathematic is deep and beautiful (literally). The concepts of fractional dimensions, bounded areas with infinite perimeters, mode-locking, bifurcations, Newton fractals - the list of new things here is staggering.
A perfect book - partly because the subject was so new to me. That said, it is a subject that is at best where physics was some three millenia back. There are infinite non-linear differential equations and the humankind is perhaps gasping at the wonders of the first few dozens. This funky math begins a proper science when some part of it can at least be mapped to a single snow-flack let alone describe water flow for a few seconds or go further to cure heart diseases or predict stock prices.
So all in all, the useability of this new science is likely to be limited in our lifetime but it is a must learn subject and this book along with Wiki opened a whole new world to me.