This is not the first time that I've tried a simple-looking technique from Natalie Chanin's book Alabama Studio Sewing + Design and been bowled over by how fabulous it looks in real life.
Here is the random-ruffled stripe, a half-inch wide strip of jersey and appliqued onto the base fabric with a running stitch down its middle. Every few stitches, you take a couple of gathering stitches which you cinch up before sewing them down to the fabric.
It's so easy and it makes such a gorgeous textural effect in real life. Try it!