Starting points

http://en.wikipedia.org/wiki/Lorenz_attractor
The Wikipedia page has the relevant equations defining what we need to do, as well as some fun images and graphs. Notably, there are also various links to implementations of the system using graphing software, Java applets, and so on. Nothing in Python, though.

http://www.pygame.org/project/617/
A simple implementation of gravity in PyGame. The equations aren't quite what we need, and the particles don't start with momentum, but it's something to build upon, and it's in the public domain.

http://www.mizuno.org/c/la/index.html
A C implementation with GNUPlot.

Other Thoughts: We were initially attracted to the Lorenz idea because it made pretty loops and illustrated chaos theory. We may very well wind up getting somewhere else once we start this project: a gravity well simulator, an abstract drawing tool, or something else along those lines. For now, we'll look at this straightforwardly, and write something toward our initial goal.

AP Final Project Proposal

Lorenz Butterflies in Python/Pygame

Thomas Doggette, Matt Yeatman

Goal: To create a two-dimensional, graphical representation of Lorenz attractors (http://en.wikipedia.org/wiki/Lorenz_attractor) in Python. The end result would be an animated system with "gravity" and particles, like the applet example at http://www.exploratorium.edu/complexity/java/lorenz.html.