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, a move north from [0, 10] reaches [63, 10], and a move east from [20, 95] reaches [20, 0]. Borders block nothing: an enemy can attack a hill near one 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

Vision, fighting and food collection all use this geometry.

Two steps show it. An ant ordered north off the top row arrives on the bottom one, and an ant ordered west off the left column arrives on the right. Nothing stops the ant or marks the crossing; its row or column jumps to the other end.

Red’s hill is in the top-left corner. Press the right arrow once: the order north takes the ant off the top row and it appears on the bottom one. Press again: the order west takes it off the left column and it appears on the right. Two steps from home, it stands in the far corner of the picture. The board has no corner to defend and no edge an enemy can pin you against.

Terrain and water

Water is impassable and permanent. A move into water leaves the ant where it was, and that ant can still collide with another ant arriving on its square. Food refuses a move the same way: an ant cannot step onto a food square, so it gathers from beside it. A land square can hold a hill and an ant together, and the engine places new food on empty land only. No two ants remain on one square after movement resolves.

Your observation keeps the water you have discovered. A zero in its water mask means land or an undiscovered square, so a route of zeros can still run into water. The observation format gives the encoding.

Hills

New ants spawn on hills and nowhere else. An enemy ant standing on a hill after combat razes it, and a razed hill is gone for good. An ant on your own hill blocks spawning there, even with food in your hive.

A colony that loses all its hills stays in the match while its ants live. They keep moving and attacking, and without a standing hill the colony cannot replace them.

Food

An ant can gather food on its own square or on one of the four squares beside it, after spawning resolves. The food goes into the colony’s hive, a shared store with no place on the map. One unit of stored food can create one ant on a free hill.

Each board puts food near the starting hills so colonies can start growing. After turn zero, food arrives at a hidden rate the engine draws from the match’s seed, between five and eleven units per colony every nineteen to thirty-seven turns. It lands in symmetric sets, so no colony is fed while its opponents starve, and a unit owed to an occupied square waits until the square is free. The rate is the one thing about a board you cannot read from its file.

Vision and fog

You see a square if its wrapped squared distance from any of your living ants is at most 77. Water does not block vision. Enemies, food and hills outside that radius are missing from the current observation, so losing an ant can hide an area you saw a turn earlier.

The engine remembers discovered water for you and nothing else out of sight: enemies, food and hills drop out of the observation once you lose sight of them. The observation carries no turn number, score or hive count. It does carry vis, the mask of what you can see this turn, so your model can tell an empty square from one it cannot see. Anything else your model carries between calls is its own memory, and only when its class allows one.

The viewer cannot show this yet. A replay frame carries the board as the referee sees it (every ant, all the water), because re-simulating an action stream rebuilds that view. replay-decode cannot yet say what a seat knew on a given turn, and until it can, a replay here would teach you the opposite of this section.

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 symmetry. The colonies choose different moves, so play can break that symmetry from the first turn.

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