White square:
Various knitting and crochet stitches all done with a knook. Open double crochets are double crochets, but minus the last yarn through, leaving a loop on the knook for each stitch. For parallel chains, I chained 3 in each loop across.

Black and purple square:
Started with a reversible, two-color slip-stitch pinwheel pattern, then did a border of double crochet around it, then did drop stitch lacework until the length was 12”, then picked up stitches along the side and did some bobbles (k, yo, k, yo, k) and then some small cables until it reached 12”. The work is a little messy looking because the hook was too large for the yarn.