#Chladni #plate #acoustic #figure #animation each frame has lines at the nodes (non-moving points) of an #eigenvector of #biharmonic #operator , successive frames have decreasing #eigenvalue .

https://media.mathr.co.uk/mathr/2019-toot-media/mathr%20-%202019-06-24%20-%20biharmonic%20eigenvectors%20chladni%20plate%20-%20256x256p4.mp4

Implemented in #GNU #Octave using its #sparse #matrix eigensystem solver. I used a 5x5 kernel for the operator, based on the 3x3 Laplacian kernel convolved with itself, not 100% sure that this is the correct way to go about it but results look reasonable-ish.

The eigensystem approach is reasonably performant (13m40s for 1000 images) but doesn't actually solve what I want to solve, which is a virtual plate being stimulated with a stereo audio signal pair to make a music video.

comparing eigenvectors of harmonic operator (Laplacian) and biharmonic operator (Laplacian squared), sorted by magnitude of eigenvalue (smallest first)

they're close, but not the same

#maths #physics #chladni #plate #acoustic #figure