The golden ratio phi = 1.618... has curious properties. On a sphere, if we make uniform steps in cosine latitude and longitude steps of 360/phi degrees, we get remarkably even distributions of points on a spherical Fibonacci spiral.pic.twitter.com/hWSk9aRnng
Is this quantified in some way? Is phi the local minimum in terms of energy of the generated points (in the space of parameters for this technique), or is it kinda close for weird reasons?
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Regardless, it is a pretty cool trick for a compressor or etc.
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Related and extremely interesting: http://extremelearning.com.au/unreasonable-effectiveness-of-quasirandom-sequences/ … especially the paragraph "Generalizing the Golden Ratio"
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Also the paragraph "Quasirandom Points on a sphere".
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Yeah, Knuth talks about this in his chapter on random number generators. Phi is sort of maximally irrational, so you don't get close to ratios of small integers that would give you strong patterns.
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It is interesting that such incredible order comes from a number that is so perfectly random.
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