Although 2D Turing Machines are no more powerful than the original ones, they’re an interesting diversion. That’s because the grid of cells enable graphical patterns to be calculated and displayed, especially if colours are written to those cells instead of letters or numbers.
Most of what we’ve learned about ordinary TMs applies to 2D TMs, the only difference being that, instead of moving only left or right, the read/write head is able to move left, right, up or down. In some implementations the movement is defined absolutely, so we can think of it as N, S, E and W, while in others it’s relative to the current direction of the head so the angle of a turn is defined as 0, 90, 180 or 270 degrees, after which the head…