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.

Yes, I was talking about solutions with special properties, like eg being optimal or minimal in some sense.

It's curious - in biology here we see similar problems solved in 3D, but it's not always clear how it's solved. Take the first few divisions during gastrulation [1] and notice that every cell divides synchronously for the first few divisions even though no single signal should be able to propagate from end to end that fast. And in other 3D environments like the sphere of cells in breast tissue you have similar synchronies that must be achieved in an environment that does not allow for rapid signal exchange (such an environment [2]).

[1] https://www.youtube.com/watch?v=4La78WtK4n8 [2] https://www.youtube.com/watch?v=3W10ywd_s6w