[capt_noonie]

The ladies are right, that is cording. It's cut on the bias (45 degree diagonal) and you sew in a cord leaving the seam allowance on the outside so you can sew it onto the pillow. Looks to me that the main part is a rectangle rolled up, and then the cording, then the ends which are also rectangles but they will be cinched up at the edge giving it the gathered look. This is very easy, but since you only have a limited amount of fabric, do a sample first in a similar weight fabric. I always to samples first, even though it seems like it would take longer, but you can't ever trust store bought patterns, they are always horrible. I don't know who pays those people to make patterns.