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arXiv · 2604.05010

The aspect ratio of the Twin Dragon is $1/\phi$

Dmitry Mekhontsev
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Abstract

We show that the geometric aspect ratio of the Twin Dragon equals $1/\varphi$, where $\varphi = (1+\sqrt{5})/2$ 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 $\varphi$ is surprising: the Twin Dragon is defined purely via the Gaussian integer $1+i$, with no pentagonal or Fibonacci structure in its construction.

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Dmitry Mekhontsev. 2026-04-06. The aspect ratio of the Twin Dragon is $1/\phi$. https://arxiv.org/abs/2604.05010

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