How to efficiently create and traverse an infinite 2D grid (Java)

Question

My assignment is this:
- At an unmarked grid location, turn left (counter-clockwise), mark the location, and move forward.
- At a marked grid location, turn right (clockwise), unmark the location, and move forward.
- there is a cap of, for example, 20000 steps of the algorithm. How can I make the grid grow to accommodate for the increasing steps?
I am just wondering:
- How can I make a grid scale infinitely in all directions
- What kind of data structure should I use for optimal efficiency (ArrayList?
)