The dramatic increase in the speed of numerical calculations made possible by electronic wizardry has opened up new vistas in school mathematics in the last few years. One application is the solution of equations by iterative procedures. Interest so far has been only on the speed of convergence of the iteration and not on how a given iteration will succeed or fail—an equally interesting area. At school level this is a relatively uncharted area, and one where a sixth-former with a calculator could produce results of interest.