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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.05541 |
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| _version_ | 1866913911163322368 |
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| author | Caprio, Danilo Antonio |
| author_facet | Caprio, Danilo Antonio |
| contents | In this work, we study properties of the coordinate functions $x_θ$ and $y_θ$ of the dragon curve associated with the angle $\fracπ{3} < θ< \frac{5π}{3}$, and we prove that the box-counting dimension of its graph is equal to $1 - \frac{\log \cosα}{\log 2}$, where $α= \frac{π- θ}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_05541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The coordinate functions of the Heighway dragon curve Caprio, Danilo Antonio Dynamical Systems In this work, we study properties of the coordinate functions $x_θ$ and $y_θ$ of the dragon curve associated with the angle $\fracπ{3} < θ< \frac{5π}{3}$, and we prove that the box-counting dimension of its graph is equal to $1 - \frac{\log \cosα}{\log 2}$, where $α= \frac{π- θ}{2}$. |
| title | The coordinate functions of the Heighway dragon curve |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2506.05541 |