  Hitomezashi, a form of traditional Japanese embroidery, gives rise to
intricate arrangements of axis-parallel unit-length stitches in the plane. Pete
studied these patterns in the context of percolation theory, and the first two
authors recently investigated additional structural properties of them. In this
paper, we establish several optimization-style results on hitomezashi patterns
and provide a complete classification of "long-stitch" hitomezashi patterns in
which stitches have length greater than 1. We also study variants in which
stitches can have directions not parallel to the coordinate axes.
