Lakes of Wada - Wada Basins

Wada Basins

Wada basins are certain special basins of attraction studied in the mathematics of non-linear systems. A basin having the property that every neighborhood of every point on the boundary of that basin intersects at least three basins is called a Wada basin, or said to have the Wada property. Unlike the Lakes of Wada, Wada basins are often disconnected.

An example of Wada basins is given by the Newton–Raphson method applied to a cubic polynomial with distinct roots, such as z3 − 1; see the picture.

A physical system that demonstrates Wada basins is the pattern of reflections between three spheres in contact--see chaotic scattering.