I assume that it is research material if you are trying to find the solution with the minimal number of states or the fastest sync time or something like that?

The two (or higher) dimensional problem if you aren't requiring some kind of optimal or minimal solution is a trivial extension of the one dimensional problem. E.g., for two dimensions, you essentially do the one dimensional solution along the top row to sync up all the elements there, and then they simultaneously start the one dimensional solution on the columns.