Love this idea. I sewed stripes together and then to the dish rag.
I'd suggest cutting edges off the edges of the dish rag or use a larger one to cut of f. I tried to sew the outside edging together, but it was too thick.
Old towels would be perfect for this project. Upcycle.
Pattern tutorial here: http://www.conniekresin.com/2011/07/dish-rug-tutorial.html?m=1