A Novel Fractal Board Game

We introduce a novel fractal board game by applying the concept of subdivision of fractals to an nxn-grid game board. Black and White place a piece by turns to compete the cell territories in the grid. As all the four vertices of a cell territory are occupied, both players score based on the number of vertices occupied by their respective game pieces on all relevant cells (sub-boards). While playing, the player with disadvantage is of right to subdivide a cell of the game board to create sub-games in a way that the subdivision of quadtree does. The game ends up if one of the termination conditions is satisfied. Due to the fact of the continuity of lines, our game board could be infinitely subdivided for generating the sub-boards (sub-games). The subdivision is used to balance the dominance of the playing-first player in the abstract board game so that there are opportunities for players with disadvantages to catch up and provides more interesting gameplay.