The Mandelbrot Set and Julia Sets

Change of Variables

Here we show how to convert a general polynomial

anzn + an-1zn-1 + an-2zn-2 + ... + a1z + a0

to the form

wn + bn-2wn-2 + ... + b1w + b0

by a simple change of variables

w = E*z + F

We procede through several steps and examples:

1. First, we eliminate an.

2. The quadratic case

3. The cubic case

4. The general case.

Return to the Mandelbrot set definition.