Introduction: Exploring Fractals

Background:

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.


(c) Copyrighted 1994,1995,1996,and 1997 by Mary Ann Connors. All rights reserved. If you wish to use any of the text or images in Exploring Fractals please contact its author Mary Ann Connors at the following address. Thank you.

Dr. Mary Ann Connors
Department of Mathematics & Statistics
Lederle Graduate Research Tower
University of Massachusetts
Amherst, MA 01003
Email:
mconnors@math.umass.edu
mconnors@math.umass.edu