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

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