Fractal Iteration and Convergence Analysis
Investigate the iterative process defined by \(z_{n+1}=z_n^2+c\) in the complex plane. Answer the following parts:
Part b
For \(c = -1\), describe qualitatively the behavior of the orbit generated by the iteration \(z_{n+1}=z_n^2-1\) starting from initial values such as \(z_0 = 0\), \(z_0 = 0.5\), and \(z_0 = 1\). What type of behavior is typically observed for orbits in this case?