Beniot Mandelbrot, the father of fractal mathematics, passed away on October 14th. Applications of fractals in fluid mechancs can be found in the phenomena of viscous fingering and turbulence.
I learned about Mandelbrot when I picked up a book on the basics of fractals . There's a great story about Mandelbrot at IBM. Hired into their research division, he discovered that the noise in the data transmission was both regular and erratic. He found that the standard approach to the noise, increasing the transmission signal, would not fix the problem [1,2]. When I first heard this story, I thought it was a fabulous example of a theoretician finding a solution to a real-world problem. Such solutions are rare, which is why pure theoretical work is hard to find at for-profit companies these days.
 Introducing Fractals: a Graphic Guide by Lesmoir-Gordon, Rood, and Edney (2009).
 Introducing Chaos: a Graphic Guide by Sarder & Abrams (2004).
 Time.com has put together a slideshow on images spawned by fractal mathematics.