Chladni figures of discrete square

Here are the Chladni figures (nodal curves) of all the eigenvectors of G=L10 x L10, a discrete square graph with 361 vertices. Click on a picture to see it larger. These pictures correspond to the classical Chladni figures on a plate one can observe when putting sand on a plate vibrating with an eigenfrequency: the sand particles rest only where the eigenfunction is zero and get thrown away at other points. See pictures like this example from MIT. The level surfaces fk = 0 for the eigenfunctions fk are in the Barycentric refinement G x K1. See the "The graph spectrum of barycentric refinements" or Sard theorem for graph for the math and mini blog, the same pictures for a triangle G3, for a triangle G3 of triangle, rounded disk, or of a polyhedron.