Laplacian eigenfunctions on a torus of revolution, color-coded and deformed to show standing wave patterns
The eigenfunctions of the Laplace-Beltrami operator on a torus provide standing wave solutions to the wave equation on that surface. This program computes these eigenfunctions numerically and visualizes them by color-coding the torus surface according to the eigenfunction’s value, with the surface geometry deformed to reflect the wave amplitude. The result reveals how the torus’s curvature influences its vibrational modes.
Controls: Click and drag to orbit, scroll to zoom.
