Wolfram Rule 30 Prizes
It is pretty hard in general to prove that calculating things takes at least O(n) time, so I wouldn't expect that one to be solved any time soon.<p>Personally, I am curious if there is any cellular automaton that has something like 3-dimensional rotational symmetry. If our universe can be described by a cellular automaton, it isn't obvious to me how such a symmetry could arise, but I wouldn't be surprised if someone figured it out.