Oh goodness, my attempts to master the double double stitch resulted in metres of scrappy, knotted thread, just as when I was trying to master the double stitch, thirty five years ago! I've deleted my last post because what I was doing was entirely wrong, and I wouldn't like to lead anyone astray. I was on the right track in thinking that what I had to master was where to bring the shuttle back in the final movement of the stitch. I have it. It comes back through the same loop of shuttle thread as the first (normal) stitch movement.
The double double stitch or balanced double stitch can be used to make a long chain or large ring that won't twist and twirl.
We had a good trip westwards to see wild flowers around the town of Springbok in Namaqualand, South Africa, which were spectacular! We were lucky, there's no guarantee when and where the flowers will be in bloom. Here are a couple of photos: