Visualization of Dynamical Systems

Welcome to the webpage on Visualization of Dynamical Systems maintained by the Nonlinear Dynamics and Time Series Analysis Group at the Max Planck Institute for the Physics of Complex Systems. Here you will find pictures, animations and programs related to our research. These encompass both introductory and more advanced themes, from both current and past projects. On each link to a project below, you will find a brief introduction to the topic as well as a more detailed description accompanying the display, where needed.

This webpage aims at being both an internal repository and a pedagogical resource, so we hope you enjoy it!

Our projects

Introduction to dynamical systems using billiards
Picture of the mushroom billiard used to illustrate chaos in a dynamical system.

The Three Body Problem
This visualization aims at introducing the problem of the movement of three celestial bodies in space in a pedagogical way.

Visualisation of a 3D Billiard
This visualization conveys the patterns of reflection of a ray of light on four spheres defining the corners of a tetrahedron.

Crystal Growth
Visualizations of different microstructure morphologies in crystal growth.

Poincaré Recurrences
Visual illustrations of Poincaré recurrences.

Programs to download

Simple Sinai Billiard
Two adjacent Sinai Billiards to play with the initial conditions

Chaotic Scattering
This visualization conveys the patterns of reflection of a ray of light on four spheres defining the corners of a tetrahedron.

Three body problem
This visualization aims at introducing the problem of the movement of three celestial bodies in space in a pedagogical way.

External links

www.dynamical-systems.org - Nice animations of mechanical systems.

serendip.brynmawr.edu/chaos/ - Java Applets of billiards.

www.apmaths.uwo.ca/~bfraser/nll/version1/ - The non-linear Lab: beautiful introduction to nonlinear dynamics.

monet.physik.unibas.ch/~elmer/pendulum/ - Pendulum lab.