Apollonian Circumcircles of IFS Fractals

Abstract

Euclidean triangles and IFS fractals seem to be disparate geometrical concepts, unless we consider the Sierpiński gasket, which is a self-similar collection of triangles. The "circumcircle" hints at a direct link, as it can be derived for three-map IFS fractals in general, defined in an Apollonian manner. Following this path, one may discover a broader relationship between polygons and IFS fractals. * * Previously titled "Explicit Bounding Circles for IFS Fractals". Some of these results appeared in the author's doctoral dissertation [14].