In this presentation, we delve into the fascinating realm of Complex Dynam ics. Originating from the work of Gaston Julia and Pierre Fatou, the Julia sets create the intricate behavior of complex functions subjected to iterative processes, yielding mesmerizing fractal images. Through understanding the behavior of points under iteration, we gain insights into their convergence patterns. This will then provide the background to prove the central theorem of this project which is the foundation for generating these fractal images known as the boundary scanning method.