TL;DR
This paper proves that all dragon curves have polygonal convex hulls and provides a complete characterization of these convex hulls, advancing understanding of their geometric properties.
Contribution
It establishes that every dragon curve's convex hull is polygonal and offers a full characterization of these convex hulls, addressing a key geometric question.
Findings
All dragon curves have polygonal convex hulls
Complete characterization of the convex hulls of dragon curves
Advances understanding of self-similar fractal geometries
Abstract
The fundamental geometry of self-similar sets becomes significantly more complex when the generating contractive maps include non-trivial rotational components. A well-known family exemplifying this complexity is that of the dragon curves in the plane. In this paper, we prove that every dragon curve has a polygonal convex hull. Moreover, we completely characterize their convex hulls.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Computational Geometry and Mesh Generation · Point processes and geometric inequalities