For this summer season I made a frilly shawl model - two narrow wool stripes in a cotton warp. When the wool shrank, the "frills" developed.
With a white cotton warp and pastel weft they look (to me) like sherbet and whipped cream...
I used linen for weft, as an earlier experiment had told me that with a cotton weft, the "frills" got too droopy.
Earlier experiments also had told me that the wool stripes would not shrink if woven in plain weave. I have experimented with warious structures for the shrinking stripes, but I have found that 2/2 twill is good enough :-)
And, yes - I have made many, many samples with my favourite wool yarn and different "programs" of my washing machine!
Be warned - different yarns give different results, and different washing machines do that, too!