Computer Graphics: Fractals generation using Mandelbrot Set with C/C++ in Code::Blocks

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." – Benoit Mandelbrot
The Mandelbrot set is created by a general technique where a function of the form
z_n+1 = f(z_n)
is used to create a series of a complex variable. In the case of the Mandelbrot, the function is
f(z_n) = z_n² + z_o
This series is generated for every initial point z_o on some partition of the complex plane separating the complex plane into two categories:

1. Points inside the Mandelbrot set
2. Points outside the Mandelbrot set