Complex Dynamics

Complex dynamics is a branch of mathematics focused on understanding how complex functions behave over time, particularly when iterated repeatedly. It studies the intricate patterns and behaviors that emerge from simple mathematical rules applied to complex numbers. This field reveals fascinating structures, such as fractals, which are infinitely detailed shapes that look similar at any scale. Complex dynamics has applications in various areas, including physics, biology, and computer graphics, as it helps explain phenomena like chaos, stability, and the evolution of systems over time.