My very first paper pieced project was a Marine Compass block that I found online. You can find this block at a website called Quilting on the Square, which has an extensive collection of compass blocks for free. What I love about this project is that you make four of the same block, rotate them, put them together, and you end up with this beautiful compass.
Carol Doak, Peggy Martin, and many other wonderful quilters create paper pieced blocks that are based on this principle.
I think that this method has a lot of potential for designing a quilt, and it is something I am exploring right now. Here is a teaser of the pattern that is coming soon.