Newton-Raphson with a Twist: Uncertainty and Fractal Basin Boundaries

摘要

In this article, James Christian makes two tweaks to the Newton-Raphson formula for computing the Nth roots of-1. By incorporating magnifications and rotations, fractals emerge that can possess a complexity far removed from John Hubbard's classic string-of-pearls patterns. Linear analysis predicts the stability of the roots, and the deep connection between fractality, uncertainty, and the butterfly effect is probed.