It's an interesting subject. Just an idea.

Result (FACTOR = 2)

As takashi said, this is really an interesting challenge.

I built a generic solution where each feature is pushed by its 5 closest neighbors weighted by the inverse of the distance and multiplied by a weight (the radius of a random circle in my case).

Note that in some cases, features may not move at all because the features surrounding them have a null cumulated effect.

The attached workspace generates 10 random circles and applies the solution to it.

Here's an example (before, after and combined):