Exploring Fractals, Pattern Formation, and Chaos Using Java

Motivation:

The following Java applets are intended to illustrate interesting aspects of fractal geometries, the intricate patterns that emerge when large systems are driven from equilibrium, and the chaotic dynamics that are common in many natural systems.

Some of the applets have been developed by Mike Cross and the others have been developed by my research group.

This explores the von Koch curve.

You can use the mouse to drag and zoom into an area of particular interest. To return back to the original view press shift-r. This curve has some interesting features: its similarity dimension is 1.26, it has an infinite perimeter, and a finite area under the curve. This program was written by John Bowen as part of an undegraduate research project in my group.

This explores the Lorenz equations.

This program was written by John Bowen as part of an undergraduate research project in my group.

This iterates a variety of 1D maps.

Here are instructions, a description of the diagnostics, and the specific equations used.

This iterates a variety of 1D maps.

Here are instructions, a description of the diagnostics, and the specific equations used.

This iterates a variety of 2D maps.

Here are instructions and the equations used.

This numerically integrates systems of nonlinear ordinary differential equations such as the Lorenz equations.

Some background:

These applets use the Java Graph Class Library developed by Leigh Brookshaw that has been modified by Mike Cross.

An archive of the source code used for the java applets on this web site will be made available soon.

This work is a continuing effort and new applets will be added as they become available. Please send me any comments or suggestions.

March 19, 2009
Mark Paul