Langton's ant highway conjecture and undecidability
From the comment: the undecidable questions are related to initial configurations with infinite support, whereas the conjecture refers to the behaviour of the ant when starting from a configuration with finite support (all but a finite number of cells are in the same initial state). If the conjecture is true then there are no undecidable problems starting from a finite support: just stop when the ant starts building the highway towards empty space.