Applications

At first fractals were just fascinating mathematical oddities. However, more and more applications have been found, such as the fractal antenna for a cellphone pictured above.

Medical advances

Lungs, AIDS, cancer, bone fractures, and heartbeats

Science

Scientists now work with fractal geometry to locate oil, identify geologic faults, and possibly predicting earthquakes.

Acid rain and corrosion can be modelled using fractal geometry. Even the big bang theory and understanding the structure of the universe can be improved with fractals.

Industry

The spring industry uses fractal geometry to test spring wire in 3 minutes instead of 3 days.

Statistical modles using fractal geometry are used to test for stress loading on oil rigs and turbulence effects on aircraft.

Image compression algorithms for storing images and retaining definition uses fractal geometry. Both the weather and the money market are very fractal in nature.

Military A fractal "footprint" can be used to identify manmade versus natural features on aerial mappings and tracking submarines.
Mother Nature

Nature fractals
Romanescu
cauliflower
Here is a funny fractal hand

Fractal landscapes

Fractals are used in movies for landscapes, dinosaur skin textures, etc. For instance, the raindrops on the skin of the dinosaurs in Jurassic Park was done using a fractal model.