Shifted Lévy's Dragon Curve and Directed Graph
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914528506150912 |
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| author | Leung, Jonathan |
| author_facet | Leung, Jonathan |
| contents | It is known that every point on Lévy's Dragon Curve admits a natural representation as a complex power series. We introduce a directed graph $\mathcal{G}_1$ which characterizes this representation. In this paper, we study the translation of the curve by $s=-1/2+i/2$. We identify another directed graph $\mathcal{G}_2$, that characterizes the translated curve and exhibits a revolving structure analogous to that of $\mathcal{G}_1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02988 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Shifted Lévy's Dragon Curve and Directed Graph Leung, Jonathan Classical Analysis and ODEs Dynamical Systems 28A80, 37B10 It is known that every point on Lévy's Dragon Curve admits a natural representation as a complex power series. We introduce a directed graph $\mathcal{G}_1$ which characterizes this representation. In this paper, we study the translation of the curve by $s=-1/2+i/2$. We identify another directed graph $\mathcal{G}_2$, that characterizes the translated curve and exhibits a revolving structure analogous to that of $\mathcal{G}_1$. |
| title | Shifted Lévy's Dragon Curve and Directed Graph |
| topic | Classical Analysis and ODEs Dynamical Systems 28A80, 37B10 |
| url | https://arxiv.org/abs/2605.02988 |