1/r attractive force by cellular automaton
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.