Avoiding Intersections of Dragon Curves
Metric Geometry
2026-01-05 v1
Abstract
This article proves that there are no self-intersections in the dragon curve when the unfolding angle is greater than 98.195{\deg}. 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{\deg}.
Cite
@article{arxiv.2601.00727,
title = {Avoiding Intersections of Dragon Curves},
author = {Reimund Albers and Zongyi Guo and Huaiyi Guo},
journal= {arXiv preprint arXiv:2601.00727},
year = {2026}
}