The shawl is wide and in order to half the stitching time the material is folded in half and stitched through two layers. This technique is often used in Rajastani tie dye pieces. I've seen only a few pieces like this done in Japan traditionally. The Japanese would go through the extra stitching to get a specific pattern. I like the mirror image actually.
Here are a few pictures of Kawamotos san's shawl from a few months back.
Ogata san is working on a simplified version. There is not the secondary middle stripe to make a separate positive/ negative section. I leave it up to you to figure out how complex you would like to stitch.
First fold the shawl in half width wise. Iron that flat. Stitch the two open sides together so it becomes a tube.
The weave is almost gauze like. A double knot can easily be pulled through the weave so a ribbon is basted on the fold side of the cloth so that the knots will not be pulled through the gauze.
Horizontal stripes are drawn on using a blue disappearing ink (Aobana) at three centimeter intervals.
When all the horizontal stripes are drawn then the wave pattern is drawn in vertically. Avoid any horizontal stretches.
You can see the brown ribbon stitched onto the right side (actual center of the opened shawl) and the two sides stitched together on the left hand side.
First the drawn lines are stitched up. When you come to a line you jump over and continue stitching from the next line over. Double knot your ends on both sides of the cloth so they can't be pulled through.
I used a black thread to make it easier to see but white thread is fine. Sew two rows between each line so that you have a row every centimeter. Drawing lines every centimeter is no fun and stitching without lines gives an overall more interesting casual appearance.
And it should look like this on the back.