Apollonian Circumcircles of IFS Fractals

The attractors of Iterated Function Systems in Euclidean space IFS fractals have been the subject of great interest for their ability to visually model a wide range of natural phenomena. Indeed computer-generated plants are often modeled using 3D IFS fractals, and thus their extent in virtual space is a fundamental question, whether for collision detection or ray tracing. A great variety of algorithms exist in the literature for finding bounding circles, polygons, or rectangles for these sets, usually tackling the easier question in 2D first, as a basis for the 3D bounding problem. The existing algorithms for finding bounding circles are mostly approximative, with significant computational and methodological complexity. We intend to hereby introduce explicit formulas for bounding circles in the plane, and some generalizations to space, thereby providing readily applicable bounding sets for IFS fractals.∗ MSC class: 28A80 (primary); 68U05, 52A27 (secondary)