The interesting question is why does this phenomenon occur when the string simulation doesn’t explicitly use the fourier series?
All that happens is each point has a displacement and velocity, and these are updated based on the distance between its adjacent points, in order to restore it back towards the center. So basically:
If i is every ith point on the string of length, then (i+1) and (i-1) act on i with some force. As every i has a horizontal displacement d and velocity v, the force on i is equal to:
- k( (di - di+1) + (di - di-1) )
where k is a hookes law spring constant. This rearranges nicely to get rid of the brackets:
k( di+1 + di-1 - 2*di)
This just means that each point is accelerated towards its adjacents, but expressed in awkward notation. I’ll draw a diagram at some point.
But yes, what motivates this really basic simulation to behave like a fourier series, and what aspect of it dictates the maximum number of apparent harmonics?