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Check out Janggi (Korean Chess), our featured variant for December, 2024.
This is very similar to a game that I have conceptualized, but never published. My own game starts with the usual 8x8 square board and the pieces arranged as usual, with all the usual rules of play, except that in lieu of moving a piece, either player may move an unoccupied square. A square may only be removed from the edge of the board (an edge cell being one with less than four orthogonally adjacent cells) and placed orthogonally adjacent to another cell.
I have a (general) rule of not publishing things here until I have programmed them for Zillions. I'm a mediocre programmer at the best of times, and when it comes to creating cells that may be moved by either player, I'm stuck. I've worked out how to make cells that only one player can move, but making them neutral and moveable for both sides is something I've had no success with.
I've thought of a similar game based on moveable hexagons.
Anyway, I'm glad to see I'm not the only one to have thought of a game with a "dynamic" board.