image credit: Amy Snyder, © Exploratorium; image source; larger image

Chaotic Pendulum

The photo above shows a three-way double pendulum at the Exploratorium, and you can see a video about this exhibit at Chaotic Pendulum. (A double pendulum is essentially one pendulum hung underneath of another--see this diagram.) In general, the motion of this pendulum is chaotic.

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Double Pendulum Model

For a simulation of the double pendulum, click here; then, in the new window, click on "download ejs mech..." and then click on the "Double Pendulum" window. Get the double pendulum started by clicking and dragging the two masses to different heights.

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image credit: Paul Bourke, University of Western Australia;  image source;
To learn more about the Lorentz attractor and chaos, visit An Introduction to Chaos.

Chaos and Fractals

Serious study of chaos began with Edward Lorenz's simplified three-equation model of the atmosphere. Visit Chaos and Fractals for a brief overview of chaos theory, including how Lorenz discovered "sensitive dependence on initial conditions", also known as "the butterfly effect." When he discovered this, he knew that long-range weather forecasting would never succeed.

(This feature was updated on September 2, 2013.)