This pattern is so named because it reminded me of the actual checkers on the board, not necessarily the straight lines of squares.
Checkerboard 2, L1-3/4—maybe a darker L4 color would enhance the pattern a bit more
It often amazes me how a change in warping can affect a pattern. In the two samples, you most likely see a pattern in the white one and no discernible pattern in the pinkish one. I used heavy and medium weight yarns in the first sample, heavy and light in the second—that may also have something to do with the appearance of the finished square.
Checkerboard 2, L1/2-4 (I think, not sure how I warped this because the ends are in very strange places)
Checkerboard 2