Complex Iteration

Using complex numbers, the process iterated to generate the Mandelbrot set 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

z_n+1 = z_n² + c

Here we reformulate the process without using complex numbers.

Next we do an example of the iteration.

Return to the Mandelbrot set definition.