chladni
Standing waves on a square plate. Drag m and n to change the mode. Bright lines are nodes — where sand would settle.
ψ(x,y) = sin(mπx) sin(nπy) − sin(nπx) sin(mπy)
Ernst Chladni put sand on a metal plate in 1787 and dragged a violin bow across the edge. Where the plate vibrated hardest, sand bounced away. Where the plate sat still — the nodal lines — sand piled up. He sketched the patterns and they're now named after him.
This is the math version. Each (m, n) pair selects a normal mode of an idealized square plate; the curve where the displacement is zero traces the figure you see above. Real plates have boundary-condition complications and nonlinear coupling — this skips all of that.