Purpose To generate nonlinear gaskets by reflection from curved mirrors; to give an optical illustration of fractal basin boundaries
Materials Three rolls of masking tape (or three sections cut from a cardboard mailing tube), four silver color aluminized plastic Christmas tree ornaments of at least 4 inch diameter, several different color folders, and (for the fractal basin boundary demonstration), a laser pointer.
Exercise Try variations: different colors and placements of lights, maybe different arrangements of the Christmas ornaments, different light levels in the room.
Conclusion Flat mirrors are reasonably easy to understand; curved mirrors have some surprises. Reflection off spheres is similar to inversion in circles. This provides some of the reason for the richness of these images. Do circle inversion fractals suggest arrangements of the reflecting spheres that might produce interesting images?