I realized it’d be much better if I referred to a general concept, instead of specific definition, just to spark ideas rather than invite challenges. The original point was to change perspectives and let foreground be background (some kind of duality - in general English) like this.
You already have a smart solution by just changing the background picture. Let me extend it and combine the Escher’s idea. Let the lines be wider and wider across the board, the stones will still be on lines (and intersections). But visually they will appear in squares. It’s still the same board, same game, and same rules.
