Unfortunately there isn't a lot out there that is like what you are looking for. Here are some books that I've read that may come close.

I like the books and essays written by Steven Strogatz, a professor at Cornell University. He's written some things intended for the general public, including a pop science book called Sync and a series of essays in the New Yorker. He also writes journal articles and textbooks. He has a way with words, of being able to describe complicated mathematical concepts without equations. Here is his website: http://www.stevenstrogatz.com

However, the two books that most awoke my love of fractals and mathematics were:

Fractals: The Patterns of Chaos: Discovering a New Aesthetic of Art, Science, and Nature by John Briggs http://www.amazon.com/Fractals-Patterns-Discovering-Aesthetic-Touchstone/dp/0671742175/

An Eye For Fractals: A Graphic And Photographic Essay by Michael Mcguire http://www.amazon.com/Eye-Fractals-Graphic-Photographic-Nonlinearity/dp/0201554402/

They are introductions. They might not go into as much depth as you want. I'm not sure a single book would.

Life in Moving Fluids by Steve Vogel of Duke University is a mixture of biology, fluid dynamics and mathematics. It can be appreciated without background knowledge, but it skips over some explanations, so probably not all of it would be accessible. But it does delve into serious depths. The first edition has more explanations than the later edition. http://www.amazon.com/Life-Moving-Fluids-Princeton-Paperbacks/dp/0691026165/

Prime Mover: A Natural History of Muscle, by the same author Steven Vogel is easier to read, but has less math. http://www.amazon.com/Prime-Mover-Natural-History-Muscle/dp/0393021262/

Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organizations by Adrian Bejan, also a professor at Duke University That's the introductory book, but if you want more detail, he has other books and scientific papers. I like his book Shape and Structure in Engineering and Nature, but it doesn't explain things very well, and a different book may be a better next step. http://www.amazon.com/Design-Nature-Constructal-Technology-Organizations/dp/0307744345/

Complex Adaptive Systems: An Introduction to comptutational models of social life (Princeton studies in complexity) by John H. Miller and Scott E. Page It was pretty readable to me, compared to textbooks in general.

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire It's an interesting topic and the book is well-written, but somehow I didn't manage to finish it. So I don't recommend it as strongly as some of the others. http://www.amazon.com/Prime-Obsession-Bernhard-Greatest-Mathematics/dp/0452285259/

Structures: Or Why Things Don't Fall Down by J.E. Gordon A good introduction to concepts of tension and compression and how they are used in buildings. Uses some math. http://www.amazon.com/Structures-Things-Dont-Fall-Down/dp/0306812835/