Let $n_{1}$, $n_{2}$, $n_{3}$ be integers, and $\phi_{1}$, $\phi_{2}$, and $\phi_{3}$ real numbers. A Lissajous figure is the curve traced by the regular path \[ \alpha(t) = (\sin(n_{1}t + \phi_{1}), \sin(n_{2}t + \phi_{2}), \sin(n_{3}t + \phi_{3})). \]
The sliders set the frequency and phase parameters. The left and right arrow keys “pan” the view point; the up and down arrow keys “tilt” the view point; comma (less-than) zooms out and period (greater-than) zooms in.