Yes, There is a Science Behind Fractals

Taken from the  HowStuffWorks website

"Fractals are a paradox. Amazingly simple, yet infinitely complex. New, but older than dirt. What are fractals? Where did they come from? Why should I care?"

"Unconventional 20th century mathematician Benoit Mandelbrot created the term fractal from the Latin word fractus (meaning irregular or fragmented) in 1975. These irregular and fragmented shapes are all around us. At their most basic, fractals are a visual expression of a repeating pattern or formula that starts out simple and gets progressively more complex." 

Books about fractals in science, math and education are available on the  Springer Website.