Avoiding Intersections of Dragon Curves

Abstract

This article proves that there are no self-intersections in the dragon curve when the unfolding angle is greater than 98.195°. This is shown by constructing a hull for the dragon curve that is mapped onto itself by the generating mappings for the dragon curve. The treatment is purely geometric. The proof is supplemented by a conjecture that reduces the boundary for the unfolding angle to 96.241°.