The fractals have more and more applications in the science. The main reason is that they describe very often better the real world than traditional mathematics and physics. Some example are presented in this page.
Cosmologists usually assume that matter is spread uniformly across space.
But observation shows this is not true. However, a dissident group of scientists claims that the structure of the universe is fractal at all scales. If this new theory is proved to be correct, even the big bang models should be adapted. More on the debate is here . Actually, the most useful use of fractals in computer science is the fractal image compression.