• Corpus ID: 235795761

Minkowski dimension of the boundaries of the lakes of Wada

  title={Minkowski dimension of the boundaries of the lakes of Wada},
  author={Zhangchi Chen},
The lakes of Wada are three disjoint simply connected domains in S2 with the counterintuitive property that they all have the same boundary. The common boundary is a indecomposable continuum. In this article we calculated the Minkowski dimension of such boundaries. The lakes constructed in the standard Cantor way has ln(6)/ ln(3) ≈ 1.6309-dimensional boundary, while in general, for any number in [1, 2] we can construct lakes with such dimensional boundaries. 

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