I was curious about the shape of an 40-variable optimisation problem with multiple minima, so I took a 2D plane through the three best local minima I'd found.   The first frame of this animation plots the score on that plane, while the later frames show what happens when I run ten optimiser steps starting from each of those points.   There is a small basin of attraction around the three minima but a lot of chaotic-looking behaviour in between.   This plot is analogous to the Newton #fractal.   
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<br />#maths #physics #optimization<p><video src='posts/202607/post-20260701-140802-a.mp4' loading='lazy' preload='metadata' controls></video></p>