【Processing】Newton Fractal given Solutions

Abstract

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Newton-Raphson's method is a method to solve an equation recursively. In addition, when we visualize it we can get an amazing fractal so I made a program that can generate fractal given point (or
complex number solution)

How it works

Generate an equation from solutions

The equation given solutions is like (x-a)(x-b)...=0. (a,b...are solution) What I should do is just calculate the coefficients of that equation. To do that I implemented multiplication of formula. This is the source code that calculate coefficients from solutions.
gist.github.com

Generate a Newton Fractal from an equation

Newton's iteration is here so I calculated differential of that coefficient.
$z_{n+1}:=z_{n}-{\frac {p(z_{n})}{p'(z_{n})}}$
gist.github.com
Finally, I visualized the number of iteration to get solutions and solutions.