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https://bost.ocks.org/mike/algorithms/
Bridson’s algorithm for Poisson-disc sampling solves your problem with using a square grid for initial point generation, it gives you uniform triangle size and randomized point distribution. Would probably really enhance the visual here.
You could also go with the best-candidate algorithm on the same page, which has the nice property of the numCandidates tuning parameter mapping nicely to the triangle variance param that's currently used to randomly distort the square grid.
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