Teachers, HS to Ph.D: physics/quantum analogies in these water-wave generators that create images?

See subject. Intriguing design-a-3D water object by water waves thing from Osaka University. I know that this could be perfect pedagogic example of something or other, and I’d like to hear how physicists or physics/science teachers would put it.

Actually, how this could be phrased for different levels of students–high school and up–interests me.

It seems like a very good demonstration of Fourier-Bessel series. The patterns in the water from each oscillator comprise a series of orthogonal basis functions, and the fact that you can “target” certain shapes is because you can take such a series for any function.

It’s not quite as impressive as it might look: The images only remain for a moment, before the waves continue on across the surface.

How would you create a standing “wave” complex? And what are the times relative to interaction of stability?

I just have this inchoate image of all sorts of fundamental forces “creating” a particle where none was before. I’m going on my understanding of such things here, which is, shall we say, inchoater.