Can cats catch mice when they walk one by one?

According to the rules of cat-and-mouse game, the mouse can walk in four directions (up, down, left and right) on each grid where the cat is located. If the cat is in the box, the mouse can only choose one of four directions to walk in the box. In this case, the cat can't catch the mouse in a limited number of steps, so the conclusion is that the cat can't catch the mouse every time it walks.