Quasicircles modulo bilipschitz maps

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On the First Eigenvalues of Free Vibrating Membranes in Conformal Regular Domains (2015, background): “On the other hand, every quasicircle can be obtained by an explicit snowflake-type construction (see [29]).”
Uniformization of Sierpiński carpets in the plane (2010, methodology): “es) are known (see, for example, [Ge1, Ge2]). Up to bi-Lipschitz equivalence all quasicircles can be constructed by a procedure similar to the one used in the deﬁnition of the von Koch snowﬂake curve [Roh]. The following proposition is essentially due to Ahlfors [Ah1]. See [LV, Ch. II, §8] for a dis”