The article focuses on the use of recursively defined fractal structures as a context for investigating mathematical induction. The paper exemplifies the use of computer experiments in visually oriented mathematics as a powerful means for engaging students and developing mathematical ways of thinking. Using Fractal Explorer, a Logo-based tool for creating and exploring fractals, the article shows how the links between key ideas in geometry, algebra, and c calculus can be made salient and visually compelling to high school students. Detailed vignettes show studentsâ€™ use of the program in intensive mathematical investigations. The Fractal Explorer employs local maps to generate fractals: rotation, translation, and contraction maps are relative to a local point associated with each iterate in the fractal structure. This contrasts with MultiMap where maps are functions defined globally on the plane. Both programs support the creation of self-similar figures that are often very ornate and beautiful. (orig.)