3. The Mandelbrot Set and Julia Sets

3. A. Complex Iteration

Using complex numbers, the process iterated to generate the Mandelbrot set and the Julia sets takes a very simple form:
z → z2 + c
where z and c are complex numbers.
To iterate the process, pick a complex number c and a complex number z0. Then generate the sequence of complex numbers z1, z2, z3, ... by
z1 = z02 + c
z2 = z12 + c
z3 = z22 + c
and in general
zn+1 = zn2 + c
How this process generates the Mandelbrot set and Julia sets is the subject of Julia Sets and the Mandelbrot Set. Here we review the mechanics of z → z2 + c.
First, we reformulate the process without using complex numbers.
Next we do an example of the iteration.

Return to the Mandelbrot set and Julia sets.