have an algo idea for this one: gradients trade colors with each other. each gradient figures out its least fitting element (high variance relative to quadratic curve) and expels it on a pile. then it picks from the pile the most fitting element. if multiple gradients want the same color, the best fit wins. if no gradient wants a color, that's a new gradient (after two consecutively unwanted colors). self-assembling gradients trading piles.
hmmm. that's almost a point cloud meshing algo...
step 1: we start with a single "gradient" that contains all colors. we fit the set to a 3d line, then sort colors by projected position on the line. then we concat all gradient groups (currently 1) back into the linear palette. the result looks ordered, but has high variance.
now the gradient has to expel its worst samples. i'll try expelling two, which form a new gradient. actually, why not find the mean variance and split the set by that.
now only letting each gradient expel 1 worst sample onto pile if variance is above threshold; each pile color is then auctioned off to the gradient whose variance it would improve the most, by a factor. then all gradients smaller than 3 are broken up and their colors put on the pile. if the pile size is >= 3, it becomes a new gradient. otherwise we run again.
clearly only the very first gradient benefits from this, others don't grow, and we end up with 104 tiny gradients.
hmhm.
obviously a gradient of 2 colors has variance 0. it's perfect. they only take on colors when the variance stays that way or gets better, so no pair-gradient ever grows.
we could make gradients bid on colors even when the variance would be worse, if the variance is still < 0.05; and we get 20 gradients, each with a variance slightly below 0.05.
the result looks like this. better, but how can this be improved further?
@lritter@mastodon.gamedev.place
new visualization.
also some rule changes: divide initial colorset into "gradients" of 16 colors each. when bidding, also bid when when the new variance is only slightly worse, or the bidder's size is 2. bidder's offer is divided by its number of colors, so long bidders lose over short bidders.
when the best bidders bid the same amount, the color is randomly awarded among them.
bidding by old-variance / new-variance rather than 1 / new-variance, i.e. not the all-over lowest variance gets picked, but the one with the most dramatic improvements.
it becomes obvious that gradients take on too many duplicates that could better serve as "crossroads" for other gradients. these should also be expelled.
hm. this should really be two parts: 1) a metric for a "good gradient" 2) gradients using the metric for both expelling and bidding on colors to judge if the change is an improvement.
also, each gradient should receive at most one new color each round so some don't take too many colors before others can bid on them.
