software for studying Newton iterates of complex map $z \mapsto -a + 1/z + b/(1+z)$

Question

I am looking for flexible software for studying complex dynamics (Julia sets, Newton iterations) with user-specified rational functions. Specifically, I wish to study the Newton iterates of complex maps such as

$g(z) = -a + 1/z + b/(1+z).$

Here $a,b$ are real parameters.

To be clear, the Newton iterations take the form: $z_0 \in \mathbb{C}$, and

$z_{n+1} = z_n - g(z_n)/g'(z_n)$.

Is there any software that can help me plot the Julia set of this complex dynamical system? Later I want to use more complicated rational functions.

Answer 1

1. mandel by Wolf Jung
2. Programs by Claude Heiland-Allen
3. console programs from code golf
4. Python program by Mihai Seba

If you know input map $p(z)$ you can compute iteration : $z_{n+1}=z_n- \frac{p(z_n)}{p'(z_n)}$ and use any program which lets you use input formula , like Xaos

HTH