I keep wondering about the dynamics of Langton's ant within an infinite adversarial environment. The game I have in mind retains the standard behavior and movement patterns of Langton's ant. However, it introduces an adversarial component: upon the ant's first encounter with any given tile, an adversary determines the initial color of the tile, either black or white. The adversary's influence is constrained to this initial tile color determination, without any additional intervention capabilities.

The adversarial objective is twofold: primary is the prevention of 'highway' construction by the ant, and secondary, if the primary objective cannot be fully achieved, is to disrupt the 'highways' as swiftly as possible post-formation.

I do not have a good intuition for who has the upper hand here. The adversary can be deliberate, but its influence is strictly limited to controlling initial conditions of the board.

Maybe this falls under the Cohen-Kong Theorem, or a potential extension of it. I'm not sure whether that applies here since the adversary may provide a board with finite support or may choose to instead provide a board (or board-generating procedure) with infinite support.