In this talk I will give a bunch of examples of what happens when you do something simple over and over again, like stretching a rectangle and folding it back on itself. These repeated simple processes, which often go under the name of “iteration” or “dynamics”, often lead to beautiful and surprising mathematical structures. Sometimes very different processes lead to the same final structure. I’ll illustrate the various examples with interactive computer programs.

This talk should be accessible to people who have had some high school math.