Chaos Theory

Chaos theory is a strange name for the niche of physics that describes the motion of most physical
systems:  fluid motion, the motion of the atmosphere,  the growth of plants and animals, and even
simple wheel sculptures.

These systems are not chaotic; they just move in complex ways.  The name was coined around
thirty years ago.  The namers liked its mysterious sound.  It is at least somewhat appropriate
because these complex motions had been thought to be actually chaotic because they were
determined by uncontrollable external circumstances: a breeze blowing on the system, a shaking
caused by a passing truck, a slight change in the temperature, somebody turning on a light. Most
physicists thought the motion would be simple in the absence of these unpredictable effects.  In fact,
the complexity was built into the system.

Only very few simple physical systems do not have complex behaviors.  A clock pendulum is an
example of a simple system.  If it is pulled away from hanging straight down, it will simply swing back
and forth in a predictable way until friction and air resistance brings it back to a stop.  The simple
motion happens because the state of the pendulum can be uniquely specified by only two quantities
and the equations that govern its motion are linear.  The definition of linear in this context is
complicated.  I will pass on by simply noting that almost everything in nature produces nonlinear
equations of motion.

As soon as one considers a nonlinear physical system for which three or more quantities are needed
to specify its state, the motion becomes complex.

The motion of the wheels in the simple example given here is computed on a laptop PC.  Such a
computer makes an error only very rarely.  I can run the demonstration shown here over and over
and always get the same result.  On the other hand, once the simulated motion has started, the
wheels can spin as long as you want to watch and they will never repeat the same motion twice.  
Never!  It is simply an infinitely complex motion.  The complexity is built into the equations of motion
even when external disturbances are absent.

Okay, I lied.  Computers represent everything using numbers with a fixed precision. When two
numbers get closer together than the precision of that computer, they are indistinguishable.  This
limitation of my computer would eventually, after a very long time, make the motion repeat.  Bummer,
but you won't watch long enough to notice.

Learn more about chaos theory in these books.
Chaos: Making a New
by James Gleick

Concentrates on the
history and the
motivation of the people
who built the science.
Chaos Theory Tamed by
Garnett Williams

Assumes basic
mathematics training, but
gives perhaps the
clearest explanation of
the technical foundations
of chaos theory.
Chaos: A Very Short
by Lenny

Assumes basic
mathematics training.  
Honoring the title, it gives
clear explanations in a
very concise format.
The Essence of Chaos
by Edward Lorenz

A best-seller by one of
the founders of chaos
theory.  Out-of-print in
paper editions, but
available as a Kindle
Copyright  2008 James W. Wiggins.  All rights reserved.
Check out a new video showing a
Chaotron kinetic sculpture
Read about chaotic motion and
the human brain