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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.05010 |
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| _version_ | 1866911622368329728 |
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| author | Mekhontsev, Dmitry |
| author_facet | Mekhontsev, Dmitry |
| contents | We show that the geometric aspect ratio of the Twin Dragon equals $1/φ$, where $φ= (1+\sqrt{5})/2$ is the golden ratio. The result follows by solving the covariance fixed-point equation for the self-similar measure, which coincides with Lebesgue area since the similarity dimension is 2. The appearance of $φ$ is surprising: the Twin Dragon is defined purely via the Gaussian integer $1+i$, with no pentagonal or Fibonacci structure in its construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05010 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The aspect ratio of the Twin Dragon is $1/ϕ$ Mekhontsev, Dmitry Dynamical Systems We show that the geometric aspect ratio of the Twin Dragon equals $1/φ$, where $φ= (1+\sqrt{5})/2$ is the golden ratio. The result follows by solving the covariance fixed-point equation for the self-similar measure, which coincides with Lebesgue area since the similarity dimension is 2. The appearance of $φ$ is surprising: the Twin Dragon is defined purely via the Gaussian integer $1+i$, with no pentagonal or Fibonacci structure in its construction. |
| title | The aspect ratio of the Twin Dragon is $1/ϕ$ |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2604.05010 |