Fractal Geometry: Uses, Math & Fascinating Patterns

[Bogrune]

The very first time I ever heard about fractals was in my junior year in high school in my Algebra II class when we were studying complex numbers. I was fascinated by these wonderous objects and I've had many questions about them ever since.
Though two of my main questions have always been: how are they used in our world, and how does Fractal Geometry describe them mathematically?

 

[Anonymous217]

I would give an answer, but I think Wikipedia does it best: http://en.wikipedia.org/wiki/Fractal_geometry

 

[Bogrune]

Well, thanks for the link. I know that many fractals can be expained mathematically by an exponential expression, but can anyone tell me what Fractal Geometry is like? Also, what does it take to comprehend it (Algebra, Trigonometry, Calculus)?

 

[TGlad]

"can anyone tell me what Fractal Geometry is like?"
Generally it is geometry that is rough, like a http://en.wikipedia.org/wiki/Koch_snowflake" .
It doesn't have to be regular, for example a coastline is fractal (over a certain range).

"How are they used in the world?"
Well fractals often are optimal in some regard, for example maximum strength to weight ratio gives fractal-like structures in bird bones and in the Eiffel tower. Maximum area coverage per length gives the fractal tree-like shape of rivers... and similarly for trees.