A website that lets you simulate and visualize almost any second order evolution equation

This is very impressive.
You remind me that I wanted to add custom equations to my complex-image transformation web-thingy for ages.

But your website is way cooler than mine will ever be lol
dope
What is the numerical method that is used?
Mathematically speaking what’s the visualization method? Finite element or something?
this is great! i like making it blow up
Very cool! Messed around a little and this was my favorite so far:

{
"laplacian": 0.5,
"cubic": 0.1,
"identity": 20,
"derivative": 0.1,
"noise": 0,
"defaultLaplacian": 40,
"defaultCubic": 1,
"defaultIdentity": 0.2,
"defaultDerivative": 0.3,
"defaultNoise": 2,
"inputStrength": 5,
"colorSensitivity": 50,
"colorMixRatio": 0.13,
"colorExponent": 1,
"colorMixExponent": 1,
"colorCap": 0.98,
"colorPattern": 1,
"scaleX": 1,
"scaleY": 1,
"scaleT": 0.02,
"maxVal": 100000,
"speed": 1,
"delay": 6,
"boundaryCondition": 2,
"useCustomEquation": false,
"equation": "u_tt = u_laplace * Delta_u \n - u_identity * sign(u) * sqrt(abs(u))\n - u_derivative * u_t \n - u_cubic * u * u * u \n + u_noise * noise \n",
"defaultEquation": "u_tt = u_laplace * Delta_u \n - u_identity * u \n - u_derivative * u_t \n - u_cubic * u * u * u \n + u_noise * noise \n",
"displayedQuantity": "u",
"initialDataFunction": "(x,y) => [0.05*y*Math.sin(0.1*x)+0.03*y*Math.sin(y),0.01*x*Math.cos(0.1*x)]"
}
I haven't worked much with PDEs of this form, but I'm interested in how you guarantee convergence of the numerical method for nonlinear F? For the numerical analysis I do, there are very specific types of schemes needed to guarantee the numerical scheme actually converges. Wondering if you have any similar theory?

Very cool idea though, the visuals do like very nice!
I pasted in that JSON but it didn't seem to update any of the parameters. Any idea what's wrong?

This looks awesome!
This is nuts hahaha I love it

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