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arXiv · 2606.05565

On the revolving structure of the L\'evy dragon and its linear transforms

Miguel Gonzalez-Carriedo·Kiko Kawamura·Jonathan Leung·R. Dániel Prokaj
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Abstract

L\'evy's Dragon Curve is a well-known self-similar fractal, notable for its ability to tile the complex plane. We review a representation of the curve as a set of points given by complex power series satisfying a revolving condition, and study how this representation changes under linear transformations, while preserving its characteristic geometric properties. We introduce a labeled directed graph that encodes these series representations and show that this directed graph remains invariant under linear transformations, with only the labeling subject to change. Furthermore, we provide a geometric characterization of the resulting variations in graph labeling.

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Miguel Gonzalez-Carriedo, Kiko Kawamura, Jonathan Leung, R. Dániel Prokaj. 2026-06-04. On the revolving structure of the L\'evy dragon and its linear transforms. https://arxiv.org/abs/2606.05565

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