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Lakes of Wada - Wikipedia

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In mathematics, the lakes of Wada (和田の湖, Wada no mizuumi) are three disjoint connected open sets of the plane or open unit square with the counterintuitive property that they all have the same boundary. In other words, for any point selected on the boundary of one of the lakes, the other two lakes' boundaries also contain that point. More than two sets with the same boundary are said to have the Wada property; examples include Wada basins in dynamical systems. This property is rare in real-world systems. The lakes of Wada were introduced by Kunizō Yoneyama (1917, page 60), who credited the discovery to Takeo Wada. His construction is similar to the construction by Brouwer (1910) of an indecomposable continuum, and in fact it is possible for the common boundary of the three sets to be an indecomposable continuum. The Lakes of Wada are formed by starting with a closed unit square of dry land, and then digging 3 lakes according to the following rule: After an infinite number of days, the

Lakes of Wada - Wikipedia Jump to content From Wikipedia, the free encyclopedia Three disjoint sets that share a common boundary This article includes a list of general references , but it lacks sufficient corresponding inline citations . Please help to improve this article by introducing more precise citations. ( February 2023 ) ( Learn how and when to remove this message ) First five stages of the lakes of Wada In mathematics , the lakes of Wada ( 和田の湖 , Wada no mizuumi ) are three disjoint connected open sets of the plane or open unit square with the counterintuitive property that they all

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