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:
human body rhythms
animal group behavior
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
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