Exploring Fractals

Fractal geometry and chaos theory are providing us with a new perspective to view the world. For centuries we've used the line as a basic building block to understand the objects around us. Chaos science uses a different geometry called fractal geometry. Fractal geometry is a new language used to describe, model and analyze complex forms found in nature.

A few things that fractals can model are: 


plants 
weather 
fluid flow 
geologic activity 
planetary orbits 
human body rhythms 
animal group behavior 
socioeconomic patterns 
music 
and more ... 
This is how nature creates a magnificent tree from a seed the size of a pea ... or broccoflower 

Fractal dimension can measure the texture and complexity of everything from coastlines to mountains to storm clouds. We can now use fractals to store photographic quality images in a tiny fraction of the space ordinarily needed. 

Fractals win prizes at graphics shows and appear on tee - shirts and calanders. Their chaotic patterns appear in many branches of science. Physicists find them on their plotters. Strange attractors with Fractal turbulence appear in celestial mechanics. Biologists diagnose dynamical diseases. Even pure mathematicians such as Bob Devaney, Heinz-Otto Peitgen and Richard Voss go on tour with slide shows and videos of their research. 

Fractals provide a different way of observing and modeling complex phenomena than Euclidean Geometry or the Calculus developed by Leibnitz and Newton. An arising cross disciplinary science of complexity coupled with the power of desktop computers brings new tools and techniques for studying real world systems. 

Strictly self-similar and not strictly self-similar shapes

The fractals that are discussed in this presentation are strictly-similar. This means that
A fractal


looks the same


over all ranges
 

of scale
 

This is called "self-similarity"