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( (d

_{i}- d_{i+1}) + (d_{i}- d_{i-1}) )

where k is a hookes law spring constant. This rearranges nicely to get rid of the brackets:

k( d

_{i+1}+ d_{i-1}- 2*d_{i})

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?