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This is fantastic, thank you!

EDIT: Just found the repo: https://github.com/Pecnut/visual-pde/

Am i right in that you use WebGL shaders not just for the presentation, but for the simulation as well?

It irks me to no end having a TLA used over and over without a definition anywhere in sight. Guessing Partial Differential Equations here?
Jumping ahead with TLAs off the top of my head to reduce future suffering:

ODE - Ordinary Differential Equations

FFT - Fast Fourier Transform

DSP - Digital Signal Processing

Thanks for posting this. These visualizations remind me a lot of Steven Lehar's resonance theory of vision. The patterns resemble learned CNN filters, but with symmetry baked in.