I've been getting myself acquainted with the Pollard Rho factorization from this page: http://www.cs.colorado.edu/~srirams/classes/doku.php/pollard_rho_tutorial.
I think I understood well almost everything that has been said, but one thing I'm confused about - the fact that we use f(x) = x^2 + a mod N to generate pseudo-random numbers for checking.
What is the usefulness of iterating f(x) and it's cycles?