Harmonic functions on a grid — eigenvectors of the graph Laplacian
The grid Laplacian L = D - A has eigenvectors φ_{m,n}(x,y) = sin(mπx/W)·sin(nπy/H) — the discrete sine transform modes. These are also the normal modes of a rectangular drumhead. Superimposing modes with time-varying phases creates standing wave interference patterns that are simultaneously musical (Chladni-like) and mathematically fundamental.