Graphing the Mandelbrot Set

The Mandelbrot set is defined as the set of complex numbers where if you take the function \(f_c(z) = z^2 + c\) and recursively evaluate it starting with \(z = 0\) and a given \(c\) where it does not diverge. We can graph this by representing each pixel with position or \(c\) value on the complex plane.