Applications of Fractals

A Few Applications of Fractals:

Noise in data transmission
This was apparently the first application of fractals: Looking at the pattern of errors that occur when computer data are transmitted electronically, Benoit Mandelbrot noticed that the errors seemed to show up in bursts. The bursts themselves were intermittent. Those shorter bursts and their gaps had a similar structure.
Distribution of stars in a galaxy
Mandelbrot made a model using only the concept of fractals and no astronomical data. His model closely resembles the hitherto inexplicable distributions of stellar matter
The positions of cars on a crowded highway
Cotton Price fluctuations in the 19th century
Studying Erosion
The rise and fall of the Nile over more than 2000 years
Metallurgy
And one of the main places you've seen fractals in use, without knowing it: Fractal geometry and computer graphics ...