Index of /~tten/Applets/ChaosGame

	Name	Last modified	Size	Description
	Parent Directory		-
	ChaosWindow.java	2013-12-29 17:34	25K
	Screen Shot.png	2013-12-29 17:34	114K

From: Dan Herbst 
Subject: RE: Posters and things for theory shows
Date: December 6, 2013 at 18:37:02  CST
To: "Thomas A. Witten" 

Hi Tom,

Here is the source file for my demo (a paltry 25 kb!). To run, 

javac ChaosWindow.java
java ChaosWindow
-Dan

Operation

Click in a red region of the rainbow window. Then look in the black window. You'll see a line that bounces around and ends up going to the bottom boundary with the rainbow strip. The exit point is in the red region of the strip.

The line represents the trajectory of a moving charged particle. The particle moves in response to a) gravity, b) an attractive charge at the green dot, and c) a repulsive charge at the red dot.

Try other starting points by clicking at other points in the rainbow window. Each time you click, a trajectory will appear in the black window. It curves in response to the the red and green charges. It bounces off the side walls. It also falls in response to gravity, eventually exiting at the bottom. The exit point corresponds to the color of the point you selected in the rainbow window.

Some regions in the rainbow are not a pure color but a jumble of colors. This means that by shifting the starting conditions just slightly, the exit point changes a lot. This "sensitivity to initial conditions" is a hallmark of CHAOS[1]. Chaos means that any change in the starting conditions, no matter how slight, leads eventually to final points that are far apart.

You can make other types of chaos by MOVING the red and green dots. The screen shot file above shows what can happen if the green dot is somewhere above the red dot. If you put the dots as shown in the screen shot and then look in the rainbow window, you will see that some regions have no color at all; they are BLACK. The screen shot is a trajectory made from one of these black starting points. As you see, the trajectory goes around and around the green dot forever and is never captured by gravity.