Does there exist a cellular automaton (in 2D) which simulates a $1/r$ force between particles?

More specifically, I would like to know whether it is possible, with strictly local update rules, to have two objects (defined within the model) attract each other with a $1/r$ force, where $r$ is the distance separating the objects.  This would in particular entail an acceleration of the object (particles) as they get closer together.

More generally, can long range attractive forces between objects (blobs) be simulated in a cellular automaton setting with strictly local rules?