# Chladni figures of discrete square

Here are the Chladni figures (nodal curves) of all the eigenvectors of G=L_{7}x L

_{7}, a discrete square graph with 169 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 f

_{k}= 0 for the eigenfunctions f

_{k}are in the Barycentric refinement G x K

_{1}. 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 G

_{3}, for a triangle G

_{3}of triangle, rounded disk, or of a polyhedron.