It is deterministic, though I am not sure if it gives one unique solution. In the example shown, there are many squares with white dots on one diagonal and blac

It is deterministic, though I am not sure if it gives one unique solution. In the example shown, there are many squares with white dots on one diagonal and black dots on the other; in these cases, it always seems to separate the white dots. (These are the cases liversage points out are ambiguous.) I guess that if you reversed the coloring, or used the alternatives for cases 5 and 10, the resulting partitioning would join the previously-white dots together. Now I am wondering if you could use the alternative for case 5 or 10, but not both.