Program windows

This is the command window for XPPAUT. Click for a fullsize image.

The data viewer, equation window, initial data window, and parameter window.

AUTO Window

Simulations windows

This is a phaseplane showing trajectories and the nullclines (red/green) for a planar ODE along with the invariant sets in blue and purple.

An integrable system colored according to energy levels.

The famous Lorenz equations projected along the coordinate axes. Click here to see it rotate.

An animated Julia set for the complex quadratic map and of course the associated Mandelbrot set

The basins of attraction for the solutions to Newton's method applied to the cube roots of unity.

Linearly coupled pendula with no friction.

Class IV cellular automata. Download the table before running ca100.ode

The Grey-Scott PDE using the method of lines and the integrator CVODE.

Animated Gifs and Toons with XPP

XPP allows you to make little cartoons using a simple scripting language so that you can create a physical representation of your ODE. Here are some same ODEs and the animation files as well as animated gifs of the simulations. Click on the miniature picture to bring up the full animation.

Here is the simple undamped pendulum rendered with the animation file.
This is a double pendulum rendered with the animation file.
Here is another way to look at the Grey-Scott equations rendered with the animation file. The curves represent the spatial profiles as of the two chemical species.
This shows the evolution of the relative phases for a 6x6 array of weakly coupled oscillators rendered with this animation file. The oscillators are nearly locked and have crossed a saddle-node bifurcation. Integrate for 80 time units and look at x33 drift.
This is a model for a waterwheel with 10 cups. In the limit as the number of cups goes to infinity, the behavior is modeled by the Lorenz equations. This cartoon is rendered by this animation file.