I have an 8x8 square(room) with an object in it at the coords of (0, 0).
If I rotate that square clockwise once, that object is now at (0, 7). I do it again an it's at (7, 7), and once more it's at (7, 0).
Which comes out as..
0, 0
0, 7
7, 7
7, 0
I'm having a hard time to figure out a formula to easily get the new object position for each rotation.
Another example would work out to this:
0, 3
3, 7
7, 3
3, 0
The point that follows $(x, y)$ is $(y, 7-x)$. Note that your second example is wrong, as $(3, 7)$ should be followed by $(7, 4)$.