Fixed Point Convergence

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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 away from the root if g'(a) < -1,
- spirals towards the root if -1 < g'(a) < 0,
- zigzags towards the root if 0 < g'(a) < 1,
- zigzags away from the root if g'(a) > 1.