This stitch pattern from the Vogue Knitting Stitchionary 2 - Cables is called Bonbons for some reason I can't imagine.
I'm hoping it qualifies under Mom's request for "simple" purple socks.
It's basically a knit 8, purl 3 rib. When stretched a little, the cables contract and pull in and the stockinette sections flair out giving a rich, wavy look to the pattern.
The cable crosses are only four stitches each, so there isn't a lot of distorting pull like there would be with an eight stitch cable cross. That's why I though the pattern might make attractive socks, and it didn't disappoint.
Pattern: Stitch pattern 128 BonBons from Vogue Knitting Stitchionary 2, Cables. Knit cuff down on 66 stitches.
Yarn: Stalwart Sock from Slackford Studio. 75% Superwash Merino, 25% Nylon 4 Ply Fingering Weight Sock Yarn.
Color: Dusk to Dawn.
Needles: Options 2.50mm circulars.
Gauge: 8 stitches/inch, 10 rows/inch in stockinette.