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Register a new userMinkowski dimension of the boundaries of the lakes of Wada
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Zhangchi Chen
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The lakes of Wada are three disjoint simply connected domains in $S^2$ 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 $ln(6)/ln(3)approx 1.6309$-dimensional boundary, while in general, for any number in $[1,2]$ we can construct lakes with such dimensional boundaries.
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