This isn't a question. This is the answer.
Someone sometime long ago and recently in Rocket Lasso Live asked for a recreation of the famous Chladni patterns in C4D.
I was randomly watching this video in Houdini and searched the term in Google.
Surprisingly there is a formula that describes the pattern.
https://physics.stackexchange.com/questions/90021/theory-behind-patterns-formed-on-chladni-plates
Following some instructions from others and searching further I found this code in Mathematica
https://math.stackexchange.com/questions/1225759/chladni-patterns
This is actually useless in C4D as it contains too many variables.
A bit more searching and found the original paper the YouTuber Junichiro Horikawa used.
http://www.phys.nthu.edu.tw/~gplab/file/07 Standing Waves/chladni patterns (US).pdf
Page 5 contains the more simplified formula.
cos(nπx/L)·cos(mπy/L) - cos(mπx/L)·cos(nπy/L) = 0
Again too many variables, but L is for length and it's kinda arbitrary to type something specific for C4D to visualize so I let it be 1. With L=1 the division doesn't contribute anything so you can totally ommit L in the formula or let it be as a placeholder if you really need to change it later.
π = pi in C4D
n and m are - acording to the paper - integers between values 1 and 5 so just replace them with something between those.
Formula generators in C4D can only get parametric equations and I don't like those.
So I used Microbion's Plotter3D
The plugin does not take the Y variable but the Z variable for height. So the final formula is (something like) this
Cos(2*pi*(x/1))*Cos(3*pi*(z/1))-Cos(3*pi*(x/1))*Cos(2*pi*(z/1)) - just change the m and n variables to something between 1-5
So there you have it
I believe it's totally possible to use XPresso to manipulate the formula string to control and have the m,n variables animate as floats between 1 - 5
Haven't tested it but if someone would like to use the output to control objects, the Plotter can generate a Vertex Map, so using Fields I think there is a chance to manipulate visibility and scale on cloners for a "sand" effect.