A Comprehensive Guide to the
Art and Science of Chaos and Complexity
What's that? You say you're hearing about "fractals"
and "chaos" all over the place, but still aren't too sure
what they are? How about a quick summary of some key concepts:
- Even the simplest systems become deeply complex
and richly beautiful when a process is "iterated" over and over,
using the results of each step as the starting point of the next.
This is how Nature creates a magnificently detailed 300-foot
redwood tree from a seed the size of your fingernail.
- Most "iterated systems" are easily simulated on computers,
but only a few are predictable and controllable. Why?
Because a tiny influence, like a "butterfly flapping its
wings," can be strangely amplified to have major
consequences such as completely changing tomorrow's
weather in a distant part of the world.
- Fractals can be magnified forever without loss of
detail, so mathematics that relies on straight
lines is useless with them. However, they give
us a new concept call "fractal dimension"which can
measure the texture and complexity of anything from coastlines
to storm clouds.
- While fractals win prices at graphic shows, their
chaotic patterns pop up in every branch of science.
Physicists find beautiful artwork coming out of their
plotters. "Strange attractors" with fractal turbulence
appear in celestial mechanics. Biologists diagnose
"dynamical diseases" when fractal rhythms fall out of
sync. Even pure mathemeticians go on tour with
dazzling videos of their research.
Think all these folks may be on to something?
