FRACTAL GEOMETRY OF RESTRICTED SETS OF CIRCLE INVERSIONS

For intersecting circles, we propose a modification of the limit set g enerated by inversion in circles. This restricted limit set is always a subset of the discs bounded by the generating circles. We give examp les of restricted limit sets and show arrangements of generating circl es for which the restricted limit set equals the limit set, and also a rrangements for which they differ. In addition, we give a visual prese ntation, based on Iterated Function Systems, of the excluded strings i n the restricted limit set. This leads to a graphical representation o f the grammatical complexity of the restricted limit set.