Cobweb diagrams of Iterated Functions

Ken Levasseur
Mathematical Sciences
UMass Lowell

Under certain conditions, a solution to the equation g(x) =x can be found by starting with an arbitrary number c and nesting the function g to produce the sequence c, g(c),g(g(c)), g(g(g(c))),. . . The graphical representation of this process is a cobweb diagram. For some functions the process converges to a fixed point, but for others it doesn't. Can you determine the conditions under which you get convergence?

Click on the Evaluate button to generate a Sage interative window with which you can experiment.


Created by Kenneth Levasseur and licensed under a Creative Commons Attribution - Noncommercial - No Derivative Works 3.0 United States License.