Research Article
On the Dynamics of Laguerre’s Iteration Method for Finding the th Roots of Unity
Figure 2
Numerically computed basins of attraction of Laguerre’s method applied to the polynomials with , , , and (row-wise, left to right). Each color corresponds to a basin of attraction of a root in the basin. The two black curves in each image are and , and the dots represent the roots of . Note how the boundary of the basin of attraction tracks but does not coincide with and appears fractal.
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