Python simulation

Follow the rules step by step, exactly as written: keep the state (a grid, a position), and work out the next state from the current one.

When every cell changes at once, build the new grid apart from the old one.

x, y = 0, 0
for move in "NNEES":
    x += {"E": 1, "W": -1}.get(move, 0)
    y += {"N": 1, "S": -1}.get(move, 0)
print(x, y)

Watch for: Changing the grid while still reading it mixes this step with the next.