The Width of a Circle

Waves are nature’s way of moving energy from here to there. Waves observed over time are cycles, repetitive motion. They’re everywhere, including the light that reaches your eyes, the sounds that you’re hearing, and the vibrations you’re feeling through your fingertips. But the world’s cycles never exist in isolation, in just a single monotonous repetition. Many simple waves meet, overlap, and interact to create complex form: a circle’s width, evolving & decaying.

These drawings are made by a harmonograph: a machine that causes multiple cycles to interact and influence one another. You can make a real harmonograph in a variety of ways: 2 (or more) linked pendulums, multiple motors, etc. Or you can get a computer to do the drawing for you, a virtual harmonograph, by plotting the interaction of 2 (or more) cyclic equations.
These harmonograph animations are projected onto custom-designed parabolic dishes. For many viewers, this helps create an optical illusion of depth from a 2-dimensional image.
In case you hadn’t guessed, I’m a physics & astronomy teacher. 🙂


Eric Muhs