Summary: xn+1 = g(xn).
The iteration converges if | g'(a) | < 1, and diverges if | g'(a) | > 1, where a is a root of x = g(x).
The iteration spirals towards the root if -1 < g'(a) < 0, and zigzags towards the root if 0 < g'(a) < 1.
The iteration spirals away from the root if g'(a) < -1, and zigzags away from the root if g'(a) > 1.