It is a well-known fact that when visualizing an IFS-attractor through the chaos game, it is possible that the first points mapped will come closer to but stay visibly different from the attractor. This simple fact will be analyzed in more detail, through visualizations of different aspects of this convergence process. It will be shown that, in applying on every point in a 2D-plane the same sequence of mappings and coloring each point according to convergence distance, neighboring points form structures which resemble the attractor itself. Further, it is in this way possible to generate boundaries of the attractor that vary between small and coarse-grained. Using these results, it will be shown that it is possible to, starting with an IFS-attractor, construct fractals of which this IFS-attractor is a subset.

VL - 13 SP - 237–244 UR - http://www.worldscientific.com/doi/abs/10.1142/S0218348X05002878 ER -