Lissajous Curves

Instructions:

Move sliders $d$ (phase-difference), $a$ or $b$ (frequencies) to change the red curve. Press the "Start" button to watch the animation, this will move the $t$ (time) slider. Press the "Stop" button to interrupt the animation and press the "Reset" button to reboot the starting values.

$$x = A \sin \left(a t + \delta \pi \right); \; y = B \sin \left(b t \right)$$

See also

Epitrochoid

Hypotrochoid

Waves sum

Rhodonea Curves