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If you have 2 periodic waves of amplitude a1 and a2 coming from different directions the peaks combine at every intersection, so there's always a grid of a1 + a2 double-peaks. If the wavelengths are around 100m, there's a double-peak every 10000 m^2 (1 hectare).

If you add a 3rd periodic wave from another direction, at any point in time some of these double-peaks will align with the peak of the 3rd wave to form a triple-peak. If you set the cutoff at a1 + a2 + 0.95a3, then about 10% of the double-peaks are triple-peaks (because cos(10% * pi) ~ 0.95).

Add a 4th orthogonal wave and about 1% are at least a1 + a2 + 0.95a3 + 0.95a4. So with 4 waves, we have a quad-peak every 100 hectares (a small farm).

Yes, this is the way. On a screen with mixed frequencies = a variable resultant. add a third dimension = voila. I knew this decades go - makes me wonder why it was missed?

you're right, I forgot that the periodic part would make a big difference!

There are a lot of waves, and a lot of time, I wouldn't discount it ever happening.

Like he chance of someone somewhere winning a lottery.

Yeah but not zero - also see two/multi photon absorption.