Within the subject of fractal geometry exist many examples of what we might call the unexpected in mathematics. Although there are many articles on fractal–building projects, one aspect of this material that provides such an example, the Contraction Mapping theorem, appears to be underrepresented. The purpose of this article is to provide a hands–on activity that illustrates this topic. We produce fractal images by iterating a set of simple rules to yield a sequence of images that in the limit consists of a fractal form. In the process, students are confronted with a surprising outcome that they actively participate in generating and that motivates a search for an explanation.
Alan Gluchoff, firstname.lastname@example.org, is interested in using fractal geometry to engage a wide spectrum of students in thinking about mathematics.