From the 'Options' tab you can choose to view Lissajous figures, Hypocyloids or Epicycloids. Use the sliders on the 'F1 and 'F2' tabs to change the parameters of the F1 and F2 harmonic motions.
Some of the more interesting figures are produced when the frequencies are different, e.g. F1 = 3, F2 = 5. If they are integrally related, e.g. F1 = 2, F2 = 3, then the pattern will be static. If they are not integrally related, e.g. F1 = 2, F2 = 3.1, then the pattern will move. You can stop this motion with the 'Free running' button on the 'Options' tab.
Changing the amplitudes is most interesting in the cases of epicycloids and hypocycloids. Changing the phase will only effect patterns which are not moving.
The drawing area of this demo is implemented as a jQuery ui widget. This is licensed for non-commercial use and you can download it here.
This is an alpha release version and the getter / setters for many options are untested. There is no documentation apart from the source code itself and the example page; however, that should be sufficient.
jQuery UI Color Picker Widget was written by Olav Andreas Lindekleiv and is available under the BSD licence hereLissajous figures, epicycloids, hypocycloids demo page Peter Frazer home page