The question is

• How is the metalball of a set of poles with random location and random radius?
• How does it evolve when we free the potential?
• How does it evolve when we free the pole center location?

This model for question 1 and 2, is by @TV . I reviewed it with current code and made a metaball User operator (new function) out of it. for the question3, I made a variation with a bounding box for the pole centers.

the user operator of the metaball the center and a radius in input and then outputs the formula of the metaball. it will be taken by the "mesh from equation" function.

the new UI for user defined feature is a must see/use. really easier than before. it is the same logic as layer of codes. when you are in the UO, you just see the UO. you can switch back and forth between main graph and UDF graph like switching folder in windows explorer. 

the logic is below. the UO is the purple feature called metaball

here is the UO

I concatenated a list of "parameterized strings". each string corresponds to a pole: R/(distance to pole center). it is equal to 1 when a point is at Rmm from the pole center. 

What/How is the metalball of a set of poles with random location and random radius?

How does it evolve when we free the potential?

How does it evolve when we free the pole center location?

there is a bounding box for the pole's centers. they are free to move inside (like us). they are bouncing on the bounding box walls.

bigger bounding box