Table of Contents

1. Newton Fractals
2. License

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:

$$z_{n+1}=z_{n}-\frac{p(z_{n})}{p'(z_{n})}$$

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.

License

newton_fractals is free software: you can redistribute it and/or
modify it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

newton_fractals is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU General Public License along
with newton_fractals.  If not, see <https://www.gnu.org/licenses/>.