Sample for new project............

I started with 6.5" squares and 1.5" strips (cut into 6.5" and 8.5" lengths) for the first round of the blocks.

Then I cut the 2.5" strips into 8.5" and 12.5" lengths.  I have the fabrics overlapped and lined up on the 1" marks of the mat so I can cut for all 4 blocks at one time.

Round 2 is sewn onto all of the blocks.

 

Then I cut each block individually in half in both directions.
 

I can use just 2 blocks and interchange the parts for 2 blocks for the quilt.

 As you can see you need to reverse the values in the blocks for it to be really effective.  If the center is light, the next round is dark, the last round is light.  If the center is dark, the next round is light and the last round is dark.  

If you always press your seams toward the darkest fabric, the seams will go in opposing directions when sewing this block together.

The option I had in mind when I started was cutting 4 blocks so I have 4 different corners in my new block. 

Some people call this block Bento Box.  The pattern I used for my Bento Box quilts had both rounds with the same size strips.  There are more variations in the strip widths if you start looking for these quilts on the internet and all of them are variations of Bento Box if we get technical about it.