Source Code
Table of Contents
Newton Fractals
This project renders Newton fractals. Given a complex polynomial \(p:\mathbb{C}\rightarrow\mathbb{C}\) and a point \(z_{0}\in\mathbb{C}\) you can apply Newton’s method to this point and see if it converges to a root. Newton’s method is iterative. It defines: \begin{equation} z_{n+1}=z_{n}-\frac{p(z_{n})}{p’(z_{n})} \end{equation} You may then ask if this converges, to which root does it converge? If there are \(N\) distinct roots, you can choose \(N\) colors corresponding to each and color \(z_{0}\) based on which point Newton’s method converges to. (If it didn’t converge, color it black. This is the Julia set of the Newton fractal).
The Newton fractal for \(p(z)=z^{3}-1\) is given below.
