So most wiki's state that it's based on the original trainers geographic locations. Also several of them state that the location is set when the game is saved the first time so it can't be changed without restarting the game.
So I have 2 theories and I'm only guessing here.
The areas of the map that have no color are less populated areas (Siberia) or areas where nintendo has little or no presence (northern Africa/Middle East/China). Not sure who created the map but they probably just didn't finish it because they didn't know what those regions produce as no one has produced one in that region yet. If this is true you will get a Vivillion based on which region you purchased the 3DS from or it's just plain unknown until someone form that specific region sets up a vivillion.
The region seems to be based on a combination of country and timezone. Timezones go by closest major city and so those regions probably are not possible to be detected by the 3ds. The 3ds will probably select the region closest within the country or on what major city the time zone is set from. If this theory is true you will get the Vivillion based on which region is closest.
Again just theories here but I couldn't find any real information to confirm these or where you got that map from.