Quilting doesn't absolutely require patchwork.

Have you ever seen Seminole patchwork? You cut strips of fabric and sew them together with really tiny stitches on a sewing machine. Then you cut new strips from the bit you sewed together and sew those strips together. It's really pretty. You don't need to have bits of fabric lying around. You have whole pieces of fabric until you are ready to work.

I have done a bunch of it and would be happy to answer any questions.