Inquiry into Fractals

The exotic images of fractals often pique the interest of high school mathematics students, and this interest presents an opportunity for geometry teachers to draw students into an investigation of transformations and patterns. By using a simple building block and fractals' self-imaging characteristic, teachers can bring construction of fractals into the high school geometry curriculum. Here, Siegrist highlights three activities that engage students in constructing a fractal, searching a fractal for patterns, and using transformations to build different fractals. In activity 1, teachers can introduce fractals by presenting general fractal facts. Images from the Internet are a good way to capture students' interest. A next step might be to illustrate how a construction matrix provides a blueprint for creating a fractal. After finishing a stage, students make two copies of that stage, one each in the upper-left and lower-right positions, to create the next stage.