I quite like this book, but it doesn't really satisfy my mathematical interest. It's far more for lay-people. But also it has some factual errors, which makes it paradoxically less use for lay people, although they'll probably never know it. E.g., the Cantor set. On page 21 it says "Any point arbitrarily close to the set must actually belong to it". This is technically wrong: the open interval (1/3,2/3) is excluded from the set, and points arbitrarily close to either end of this interval are NOT in the Cantor set (and the same for every smaller excluded interval ad infinitum, not to mention the open sets to the left and right of the Cantor set). Then on p.22 we have a hopelessly inadequate description of the Peano curve, which you can improve upon simply from Wiki - the whole (fractal) point is that Peano took a pattern that could be repeated to infinity at smaller and smaller scales, thus filling the entire two-dimensional plane with a one-dimensional line. After that things aren't so bad, although the maths of the Julia and Mandelbrot sets is interesting, so it's a shame it had to be missed out. Clouds and coastlines and stuff were what interested me, as I hadn't covered them, and the book does a fairly nice job with them and with the Hausdorff dimension (although again the book's use of logarithms is bizarre - the fractal dimension is the log, to the base 'scale-factor', of the repetitions. To divide the log of the repetitions by the log of the scale-factor is merely a shortcut you can use to calculate the actual logarithm).
It looked as though the information density was such that the book would contain a huge amount of info. But then after about the half-way mark it gets thinner on the ground, starting with a diffused biography of Mandelbrot, which didn't interest me much, and the second half of the book contained far less information than I hoped. It was just basically a list of assertions of vaguely related phenomena, a lot of which didn't really have much to do with fractals, as far as I could see - in fact, the meaning of the word "fractal" seemed to morph into "anything that isn't classical", which doesn't really help the subject much. It looked at economics, which is a subject that interests me, although I have no knowledge of it, and a closer, slightly more theoretical look at it would have suited me down to the ground.
My suggestion to lay-people trying to understand mathematical ideas is, if you're interested in maths, why don't you study maths? You would really benefit from it. There are night schools, and there is the Open University. Think about it. I'm thinking of studying economics.