From the Akiyama *et al.* paper ([arXiv abstract][1]) which Gerry cites,
Figs. 10b and 12b,
both factal limit cases with ratio $r = 1/\phi$:
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![Fig.10b][2]
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![Fig.12b][3]
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  [1]: http://arxiv.org/abs/1001.4203
  [2]: https://i.sstatic.net/hkkKD.png
  [3]: https://i.sstatic.net/Zi0hA.png