Non-self-intersective dragon curves

Abstract

Let us fold a strip of paper many times in the same direction, and then unfold it to form a fixed angle $\theta$ at all creases. The resulting shape is called the Dragon curve with the unfolding angle $\theta$. When $0\le\theta<90^{\circ}$, the corresponding Dragon curve has a self-intersection. When $\theta=180^{\circ}$, the corresponding Dragon curve is a straight line, which has no self-intersection. In this paper, we will show that any Dragon curve whose unfolding angle is greater than $99.3438^{\circ}$ and less than $180^{\circ}$ has no self-intersection.