"If we sample a moment from music and analyze it in terms of its fundamental frequency and associated harmonics, and then apply that sample to, say, a circular latex membrane of known elasticity, known diameter and fixed edge, present mathematical techniques cannot predict what pattern will form on the membrane."<p>If you knew the resonate frequency of the membrane I wouldn't think this would be that hard to figure out using Fourier analysis <a href="http://en.wikipedia.org/wiki/Fourier_analysis" rel="nofollow">http://en.wikipedia.org/wiki/Fourier_analysis</a>