Harmonograph

A harmonograph consists of a pen attached to two damped pendulums. Manipulate the parameters to see their affect on the resulting plot. For random settings, the plot is likely to appear chaotic. The best images come from and frequencies that are harmonics of one another or are very close to one another. The snapshots show plots for special cases of the harmonograph that match our intuition. The formulas used to generate the plot are:

,

.

For a YouTube video demonstrating a harmonograph, see http://www.youtube.com/watch?v=H4YQonwQUDs&feature=player_embedded.

For a picture of a harmonograph, see http://www.karlsims.com/harmonograph/index.html.