This pattern comes off the square layout and into a hexagonal layout, there are 3 branches to each spiral which gives is natural flex in different planes. (svg here)
All of this is interesting but I mentioned before that most of the flex comes from the base material. I've attached a picture of it here, because it is just 0.8mm thick it can already perform incredible bends that you wouldn't expect from plywood. I'm fairly sure that 90% of the stuff done with living hinges could just be done with this ply, no need for additional cutting.