The aspect ratio of the Twin Dragon is 1/φ
Abstract
We show that the geometric aspect ratio of the Twin Dragon equals 1/, where = (1+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 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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