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 $\hat{I}¸$ at all creases. The resulting shape is called the Dragon curve with the unfolding angle $\hat{I}¸$. When $0\le \hat{I}¸<90^{\circ }$, the corresponding Dragon curve has a self-intersection. When $\hat{I}¸=180^{\circ }$, 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.