Applets
by
Chris Sinclair

Java applets are small applications which can be run within web pages. Your computer must be capable to handle Java in order to run any of the following applets. These applets have interesting mathematical content and most are accessible to even the math-illiterate.

Java is a new language, and thus you may experience difficulties running some of these applets on your computer!


The Enigma Applet
This applet reproduces the behavior of the German World War II Enigma device. Enigma was a secret message encoder and decoder that relied on an interesting mathematical property to encrypt and decrypt messages. With this applet, you can encode messages and see how the device worked.

Penrose Nets from Quasicrystals
This applet shows a relationship between a physical phenomenon known as a quasicrystal, and aperiodic tilings of the plane. This applet is currently a research tool, and may bog down many computers. Though the title of this applet may seem daunting, it produces beautiful images as well as explores a research frontier in mathematics.

Phase Portraits of Linear Systems
This applet allows one to explore the phase spaces associated with two dimensional linear ordinary differential equations. Such equations are used to model the oscillation of springs, and simple models in population dynamics. Examples of all types of fixed points in two dimensional ODE's are provided as well.

Phase Portraits of Two Dimensional Systems
This applet allows one to imput an arbitrary two dimensional system of differential equations and see associated trajectories. The applet uses the Runga-Kutta 4 algorithm to compute the trajectories.

The Area Preserving Henon System
The Henon system is a symple recursive map which produces very complicated dynamics. An exceptional example of a fractal arising from dynamical systems, with this applet you can explore its various fractal properties. Stunning images can be created by clicking in the viewing area, or employing the escape time algorythm.This applet was among my earliest, and can be computationally intensive (esp. the escape time button) so use at your own risk!

The Henon Strange Attractor
Through this applet one can explore a strange attractor. Strange attractors are complicated geometric structures which can arise in a variety of settings. Strange Attractors are related to fractals; this example comes from a dissipative interated map of the plane.

Diffraction Patterns
Poke holes in a virtual diffraction screen and see the far-field diffraction pattern that is formed. Take care not to poke too many holes (or decrease the pixel size too much) or this applet may bog down your machine!


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