The image below shows four copies of the 8th iterate of the Heighway dragon (the backstitch design uses the 12th iterate so the orientation of the first segments are in a different direction than in the image). Click on the play button to see an animation of the iterates starting at the beginning of each curve that demonstrates how each of the four iterates consist of line segments that intersect only at corners and never cross. The three buttons labeled slow, normal, and fast will adjust the drawing speed.