What's the general strategy/approach for defining the basins of attraction within the Newton-Raphson(NR) function in the complex plane? I would like to understand where these are to colour-in a NR fractal. I hear that's its possible to discover basins by iterating some number of times around a point- but what if there are thousands of points? would I have to run the model twice (once for basin inference and then again for the plot?).
For example:-
(a) What are the (two) basins of attraction for: $f(z) = \frac{z^2 - 1}{2z}$
(b) How did you arrive at them?
Forgive me if I sound stupid- I know full well that I am no mathematician.