I don't have a good intuition of what the multiple strings are supposed to mean. Perhaps I'm seeing a bug because the initial "pull" seems to come from the bottom of the screen instead of the middle.
The 2D water wave should be displayed with more contrast. I can see a vague movement, but the peaks and troughs mostly just blend in with the rest of the water.
The code "pulls" the middle sample down, to the bottom of the window, and then the simulation runs.
As for the 2D simulation, you were right - I just pushed a version with more contrast.
Thanks for the feedback!
Actually, that's exactly what you are seeing - by pulling the middle sample down to the bottom every time you click, the "spring-like" pull of the sample to the left and the sample to the right (see the Theory section) trigger additional waves that propagate, reflect on the walls, and interfere with the original one.