Traveling rib motif from Teva Durham's Slinky Tree Bark Rib Tunic (in the book Loop-d-Loop: More Than 40 Novel Designs for Knitters)

This isn't a beanie, as you've noticed, but the beginning is the same, and if I'd had more yarn, it could have become a beanie. I'm calling it a neckwarmer even though this tube can be used as a headband, and earwarmer, or an added layer with a hat.

I used a cable cast-on (done on size 8 needles), started the ribbing with one motif repeat, and then added in the second motif repeat on the other side of the tube about 3 inches up. I knit until I ran out of yarn; next time I'll make this long enough to pull up over the nose and mouth (combined with the beanie I knit for this set, the effect would be quite ninja-like). This is long enough to tuck into a shirt collar and pull up to the chin.