Say I take a cord, tie a loose knot in three-dimensional space, and pull tightly on the ends to generate an approximation of an ideal knot. If the cord has a fixed knot topology and a random initial configuration in space, are there any conditions under which I am guaranteed to generate a particular ideal knot approximation? In other words, if I perform something akin to simulated annealing to approximate the ideal knot, is it possible for me to always arrive at the same final state (whatever that may be) within some small error?

[Sept. 29th, 2011] - Are there any conditions/constraints under which I might be able to reliably achieve some local (or global) minima in the energy landscape of a knot?

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