This project draws the Lissajous Curve family with the equations: X(t)=Asin(at+delta) Y(t)=Bcos(bt) Try A=B=100 and a=50 delta=70 b=40 for an interesting instance. You can also use the sliders in Turbo Mode to see what each parameter does to the curve.
This work was inspired by leszpioPL's fantastic curve animations.