1/r attractive force by cellular automaton

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?

If by "simulate" you mean something like "generate a picture of what the dynamics would be under such a force," then the answer to your question is yes: there exist universal cellular automata (including Conway's original Game of Life rule set).

If, however, you're asking about whether our universe can be explained in terms of strictly local update rules, then your question is still open. Konrad Zuse was one of the first to explore this question explicitly in terms of CA; see Wolfram, Schmidhuber, or t'Hooft for more recent work.

StackExchange Computer Science Q#11933, answer score: 3