The world

The Ants world is a rectangular grid of land and water. Coordinates are [row, column], both starting at zero. The observation’s size gives [rows, columns]; do not assume a square board.

The grid, and why it wraps

Both axes wrap. On a 64 × 96 board, moving north from [0, 10] reaches [63, 10], and moving east from [20, 95] reaches [20, 0]. A border is not a wall, and a hill near it can be attacked from across the board boundary.

Ranges use the shorter wrapped displacement on each axis. With row difference dr and column difference dc, use:

dr = min(abs(r1 - r2), rows - abs(r1 - r2))
dc = min(abs(c1 - c2), cols - abs(c1 - c2))
distance_squared = dr * dr + dc * dc

This same geometry controls vision, fighting, and food collection.

Six steps are enough to show it: an ant ordered north off the top row arrives on the bottom one, and west off the left column arrives on the right. Nothing stops it and nothing announces it — the row or column simply changes ends.

Six orders, three north then three west, and both edges are crossed: turn 1 puts the ant on the top row and turn 2 has it on the bottom; turn 4 puts it in the left column and turn 5 has it on the right. It ends in the far corner of the picture, three rows and three columns from the hill it started on — six steps from home, having walked six. There are no corners to defend and no edge to be pinned against.

Terrain and water

Water is impassable and permanent. A move into water leaves the ant where it was; that ant can still collide with another ant arriving there. Food refuses a move the same way: an ant cannot step onto a food square, so it gathers from beside it. Land can carry a hill and an ant together, and new food is only ever placed on empty land. Two ants cannot remain on one square after movement resolves.

The observation remembers water you have discovered. A zero in its water mask means either land or an undiscovered square; it does not certify that a route is clear. See the observation format for the encoding.

Hills

Hills are the only places new ants spawn. A surviving enemy ant razes a hill by standing on it after combat. A razed hill is gone permanently. An ant on your own hill blocks spawning there, even when food is available in your hive.

Losing all hills does not immediately eliminate a colony. Living ants continue to move and attack, but cannot be replaced without a standing hill.

Food

Food on or directly beside an ant can be gathered after spawning resolves. It enters the colony’s hive, a shared store rather than a map location. One unit of stored food can create one ant on a free hill. Food placed near starting hills helps colonies begin growing; new food is placed symmetrically as play proceeds.

Vision and fog

A square is visible if its wrapped squared distance from any of your living ants is at most 77. Water does not block this radius. Enemies, food, and hills outside it are absent from the current observation. Losing an ant can therefore hide an area you could see a turn earlier.

The engine remembers discovered water for you. It does not retain out-of-sight enemies, food, or hills in the observation. There is no turn number, score, hive count, explicit visibility mask, or model state carried between calls.

The viewer cannot show this yet. A replay frame carries the board as the referee sees it — every ant, all the water — because that is what re-simulating an action stream reconstructs. What a seat knew at a turn is a different thing, and replay-decode does not answer it. Until it does, a replay here would show the opposite of the point.

Symmetry and boards

Every seat starts on the same board: seat k’s terrain, hills and turn-zero food are seat 0’s moved k times by the board’s shift, which the map file names as symmetry. Play can break that symmetry immediately because the colonies choose different moves. Symmetric starts do not imply identical outcomes.

The board determines dimensions, terrain, hills a seat and seat count. Boards seat from two players to eight, a season’s boards are its own, and two of one size can seat different counts — so read the seat count from the board, never infer it from its size.