👉 Have you ever heard about Chladni figures? And have you ever actually heard, and seen, Chladni figures? Tomorrow is your chance! Look at what fun we've been having setting this up for you. And for those of you who want some theory:
https://en.wikipedia.org/wiki/Ernst_Chladni#Chladni_figures
#ndwgoe #ndwgoemps #mpsgoettingen #goettingen #chladni #vibrations #physics
#harmonics #cymatics #flsstudio #fruityloopsstudio #jungle #dnb #drumbass #audio #bass #artist #chladni #resonance #physics
Math behind Vibrating Sand: #Chladni Figures, paper with #math at https://ms-math-computer.science/preprint/2016_SRP_Chladni.pdf #implicitformula #periodicstructures
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
#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.
