FRACTAL GEOMETRY OF RESTRICTED SETS OF CIRCLE INVERSIONS

Abstract

For intersecting circles, we propose a modification of the limit set generated by inversion in circles. This restricted limit set is always a subset of the discs bounded by the generating circles. We give examples of restricted limit sets and show arrangements of generating circles for which the restricted limit set equals the limit set, and also arrangements for which they differ. In addition, we give a visual presentation, based on Iterated Function Systems, of the excluded strings in the restricted limit set. This leads to a graphical representation of the grammatical complexity of the restricted limit set.