http://nano.caltech.edu/publications/papers/Matheny-2019-Sci...

Looks like they did simulate it, and the experimental results differed from the simulation due to number of harmonic terms used: “To obtain quantitative agreement between the phase model (Eq. 3) and the experiment, additional terms in the harmonics of the magnitudes would need to be included in the phase model.” Which I suppose implies that very weak, distant harmonics might play an important role in these patterns.

Also an earlier paper from the same group that discusses infeasibility of other approaches: https://authors.library.caltech.edu/81293/1/acs.nanolett.7b0...