Minpentai

“For each 2x2 block, if exactly 3 cells filled, rotate 180°.”

The board is cut into two-by-two blocks. On even turns the cut begins at the corner; on odd turns it shifts one cell down and one across, so every block is stitched to its neighbours. A block holding exactly three stones turns half a revolution. Every other block holds still.

Nothing is created and nothing is lost. The rule is its own inverse: apply it twice under the same partition and the board is exactly as it was.

// board: 32×32 bits packed into uint256[4]
// even turn: tiling at (0,0) · odd turn: (1,1)
function step(uint256[4] memory b, uint256 turn)
    internal pure returns (uint256[4] memory n)
{
    n = b;
    uint256 o = turn & 1;
    for (uint256 y = 0; y < 32; y += 2) {
        for (uint256 x = 0; x < 32; x += 2) {
            uint256 x0 = (x + o) & 31; uint256 x1 = (x0 + 1) & 31;
            uint256 y0 = (y + o) & 31; uint256 y1 = (y0 + 1) & 31;
            uint256 tl = get(b, x0, y0); uint256 tr = get(b, x1, y0);
            uint256 bl = get(b, x0, y1); uint256 br = get(b, x1, y1);
            if (tl + tr + bl + br == 3) {
                // rotate 180°: tl↔br, tr↔bl
                n = put(n, x0, y0, br); n = put(n, x1, y1, tl);
                n = put(n, x1, y0, bl); n = put(n, x0, y1, tr);
            }
        }
    }
}

Step back undoes the last turn by applying the rule again under that turn’s partition. There is no history kept, and none is needed. The sandbox wraps at its edges.

Twice is never

A four-by-four board, cut at the corner. Two of its blocks hold exactly three stones; the other two do not.

The rule is its own inverse: applied twice under the same partition, every state returns.

One thousand and twenty-four cells, packed into four 256-bit words. Each player’s symbol is revealed onto opposite corners — A at the bottom-left, B at the top-right — and from there the rule does the rest.

Grid

32 × 32, square

Storage

uint256[4]

Seeds

One 3×3 symbol per player, opposite corners

Reach

New stones within Chebyshev distance 30 of a live copy of your symbol

You are looking at what your identity would look like on the board.