Use Lissajous Play to explore Lissajous figures by adjusting all the variable parameter to your desires.

The basics are that there are two sine waves being used to determine the plot coordinates, one driving the x value and the other driving the y value. If these are in phase, and the same frequency, then you get a stright diagonal line; push the y data 90º (π/4 radians) out of phase and you get a circle.

The phase slider lets you vary the phase between 0-360º ( 0 - 2π radians)

With the x & y frequencies as Integers the Lissajous will be a closed loop.

Varying the x&y frequencies will produce interesting shapes with which you can animate the phase, or watch the shape traced out over time.

If the line length is at max then a closed loop shape will only trace once. If one, or both, of the frequencies are not intergers then things get interesting, as it's not a closed loop the trace will continue to draw and get more complex, adjusting the phase adds even more interest.

Adjust the background/plot colours, line width/shadow, to pleasing artistic effect.

A must have for physics and engineering students, or just for interest and fun.

Have fun, and share your work...