The pattern on each side of the small of the leg is called "svikkel". And it was "designed" to disguise and cover the ankle knuckles. They are not particularly pretty, perhaps even ugly but the purl patterns transform your leg into a slim, delicate part of your body.
I cannot publish the pattern, however if you want to knit a pair like this you can follow this recipe:
Old Danish Folk Sock
You will need 100 g of fingering sock yarn in natural, blue, or black.
A set of 5 dpn needles size 2 mm or 2,25 mm
A vanilla sock pattern, there is one here on this site.
An original sock pattern. On this website you will find two different patterns on page two.
Cast on the amount of stitches from the vanilla pattern on four needles, and work the border from the Danish pattern.
Continue with stockinette stitch and seam pattern for a couple of cm. Skip all the increases and decreases.
Begin the "svikkel" pattern using this trick: the center of the first pattern is the first stitch on needle 2 and the last stitch on needle 3 is the center of the second pattern.. Remember to start from the top of the chart or turn it upside down.