Here's what happens if, after each optimisation step, every point is averaged with its neighbours.  This encourages the formation of basins around various local minima and the colours at the borders give some idea of the barrier heights between them.  This is a little too dynamic at present, it looks like a bubbling cauldron, and I forgot to anchor the original 3 local minima so one of them disappears under the bubbling, but it looks like it could be a promising visualisation of part of a 40-dimensional optimisation landscape.
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<br />#optimization #maths #physics <p><video src='posts/202607/post-20260706-160117-a.mp4' loading='lazy' preload='metadata' controls></video></p>