Here are some different shapes that a hydrogen atom can take. These plots are based on the same function as the vibrating balloon :

*P = 4 π r*^{2}ψ_{r}^{2}ψ_{θ}^{2}, ψ_{r} = e^{-ρ}ρ^{l}L_{n-1-l}^{2l+1}(ρ), ψ_{θ} = Y_{l}^{m}(θ,φ), ρ = 2r/n

`(* runtime: ggg second *)`

P[n_, l_, m_, {x_, y_, z_}] := Module[{r = Sqrt[x^2 + y^2 + z^2]}, 4 Pi r^2(Exp[-r/n]r^l LaguerreL[n - 1 - l, 2l + 1, 2 r/n])^2 Abs[SphericalHarmonicY[l, m, ArcCos[z/r], ArcTan[x, y]]]^2];

DensityPlot[P[3, 1, 0, {x, 0, z}], {x, -20, 20}, {z, -20, 20}, Mesh -> False, PlotPoints -> 275, Frame -> False, Compiled -> False]

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Dear Paul Nylander,

I very much appreciate your blog and associated some of your ideas with cymatics and water reorientation and skateboarding. I love to skate and find a variety of interests from cymatics, fractals and physcis to cultural appreciation from around the world. I created a post called “Cymatic skateboards and water reorientation” as a liberal and humanitarian art work and scientific challenge to perhaps assist others in the study of hydrology, browns gas, quantum physics, applying fractals in practical engineering, experimenting with ultra violet black light emissions or cymatics as alternatives in wave theory dynamics in a chaotic model for process engineering, etc.

Those hydrogen orbitals are beautiful!

Symmetry and periodicity!

Have you seen this on-line book?

http://cns-alumni.bu.edu/~slehar/HRezBook/HRezBook.html

Harmonic Resonance is a pretty magical property of physical matter!

Steve

very beautifull…but the link of vibrating balloon doesn’t works ?