Grasshopper

algorithmic modeling for Rhino

Is there any way to cluster circles with attractors by density? 

I'm having a lot of trouble preventing the circles from overlapping each other.

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If you want to ensure that circles with a given centre do not overlap, you can limit their radii to half the distance to the nearest other circle centre point. However, this solution is usually not satisfactory as circles end up being smaller than absolutely necessary. You can use Proximity3D to find the distances for each point to its nearest neighbour:

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