x=sin(at+δ), y=sin(bt), z=sin(ct+φ) — three coupled sinusoids create beautiful space curves. Integer frequency ratios produce closed curves; irrational ratios densely fill a torus. Drag to rotate.
Jules Antoine Lissajous (1857) used tuning forks and mirrors to produce these curves optically. In 3D, the curves trace paths on tori and link theory — T(2,3) produces the trefoil knot when a=2,b=3,c=0. Use "animate phase" to watch the curve morph continuously.