AMITA Why am I the only one fascinated by these? You worship Knox. When you taught Ergodic Theory, you lectured for two weeks on his work...

ALAN They're making progress... CHARLIE We found the point of convergence. (a nod toward Bloom)

This Demonstration shows the convergence properties of a family of Newton-like methods for computing square roots of positive reals as constructed by
Hernandez and Romero. In this Demonstration the roots of 35 are used. For each integer *q* > 2, the iterative
formula (displayed in the top left-hand corner) is defined. It generates a sequence (displayed below the formula)
converging to one of the roots of 35 for almost all chosen starting values in the complex plane, outside the imaginary
axis. The initial point is shown in purple, the two roots (limit points) are colored yellow, and some of the
intermediate points are colored in shades of yellow, with darker colors corresponding to later positions in the
sequence.