A little late to the party, but maybe interesting

Thanks for the reply and code.

I played with this a little and it definitely produces clumps. The problem with it (for my purposes) is that it always leaves a background of relatively uniformly distributed points, and I couldn't see any way of preventing that.

For my purpose, I really want clear space around and between the clumps, which the weight map method both achieves and gives fine control over.

However, your "attractors" idea sparked another idea in me -- completely unrelated to OP purpose -- but intriguing enough to sidetrack me for a day or so.

What happens if you treat a set of clumpy random points as equally sized particles of some finite mass, and have them all exert "gravity" upon each other according to the inverse square of their distance.

Tada. The red dots are the starting position, the cyan their position after a single round of attraction, and the blue, after the second.

Ignore the ones that 'sling-shot' off into outer space; the effect of the inverse square law is that in order to get detectable influence over any distance, you have to set the mass of the points quite high, with the consequence that once they get very close to each other, they exert huge forces that results in sling shots because there are no collisions.

Over many generations, the gravity will cause all the points to come together (and then be scattered in all directions), but the first few generations have the effect of concentrating whatever clusters already exist. I wonder if this wouldn't be a fruitful technique for tackling the NP-hard clustering problem without resorting making assumptions per the K-means type of algorithm?