Apollonian Circumcircles of IFS Fractals
J\'ozsef Vass
TL;DR
This paper explores the relationship between Euclidean triangles, IFS fractals, and circumcircles, introducing an Apollonian approach to connect polygons with fractals.
Contribution
It introduces a method to define circumcircles for three-map IFS fractals, revealing a broader link between polygons and self-similar fractal structures.
Findings
Circumcircles can be derived for three-map IFS fractals using an Apollonian approach
A broader relationship between polygons and IFS fractals is established
The approach links classical geometry with fractal self-similarity
Abstract
Euclidean triangles and IFS fractals seem to be disparate geometrical concepts, unless we consider the Sierpi\'{n}ski 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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Neural Networks and Applications · Cellular Automata and Applications