#
What is a Chaotic System?

This intro to chaos theory with Java applets was written by Ben Fisch, as
part of a 2009 summer project at PPPL working with Luc Peterson and Greg
Hammett, based on a chaos tutorial by Charles Karney.

(There are some bugs: Some of the control boxes don't appear until you
click on a figure or in some of the empty space around a figure.)

## Consider frictionless balls in a square box:

###
One Ball, One Box

In this first demonstration, a single ball with some constant
velocity, mass, and radius will move around inside the box and bounce off the walls.

This is an example of regular motion. The ball's motion is restricted to 4 different directions.
The ball's position at any given time is easily predicted.

###
Two Balls, One Box

Now we place two balls in the box, very close to each other.

We give the second ball a slightly different velocity. (30.5 compared to 30).

You can see the separation of the balls grow slowly.
(WE IGNORE COLLISIONS BETWEEN THE TWO BALLS. THEY PASS THROUGH EACH OTHER.)

This is still regular motion.

####
Characteristics of Regular Motion:

1.) Motion of each ball is restricted.

2.) Errors (i.e. imprecisions in ball velocity) grow slowly.

3.) Even given errors, it is possible to predict the balls' trajectories
and positions for a fairly long time.

###
Round One Corner

Now we round one corner, expanding the possible directions of motion.