Elementary Fractal Geometry 7: An Algorithm Visualizing the Magnification Flow

Self-similar sets are defined as compact attractors. Their interior structure, however, is revealed only by successive magnification. This requires the use of a computer. We describe a new and very simple algorithm which performs an unlimited magnification of self-similar sets. In the case of integer data, it works without numerical error propagation. In other words, the program visualizes the scenery flow introduced by Bedford and Fisher, and Hochman. An open-source MATLAB implementation of the program is provided as a starting point and invitation to computational work in fractals.