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; larger image

Chaos Theory: A Brief Introduction

This image shows the "Lorentz attractor," a graph that represents the behavior of a simple model of Earth's weather. Weather is just one example of a chaotic system, in which seemingly irregular behavior does follow certain patterns.

For an overview of chaos theory that concisely explains the characteristics of chaotic systems, see Chaos Theory: A Brief Introduction.

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.

To learn more about Lorenz and also about the chaos of population dynamics, see Chaos Rules, from the American Physical Society outreach website Physics Central.