First talk is by me, @msmathcomputer. I am speaking about the generalization of #Chladni figures to the third dimension. Thereby, the intersection of sound waves becomes tangible, e.g., in the form of a #3dprint. https://www.youtube.com/watch?v=hiz1CboQP3U&list=PLIQnnJvM8OOkmbjgyRy_Bpbxl0JjM8eyp. (2/5)

1/60s loop with RMS low pass filter set to 60/32Hz. video is the fake-#Chladni-#plate algorithm (which I think solves the #harmonic operator not the #biharmonic operator) I found online and implemented in #GLSL

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

#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 .

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.