I'm trying to do my math IA on the effect of changing complex constant c in the mandelbrot set on the series's convergence, but I don't know how to algebraically solve the limits for iterative functions, even when I can do so graphically and in tabular form.
For example, how do I algebraically find the limit to $x_n = x_{n-1}^2 - 0.6$, which I know graphically approaches $0.42$ at infinity?