Exploring the Dynamics of the Circumcenter Map

TL;DR

This paper investigates the properties and topological features of the circumcenter map, which iteratively transforms polygons into scaled and rotated copies, revealing insights into its area-expanding and contracting regions.

Contribution

It introduces an experimental analysis of the circumcenter map's dynamics and topology, highlighting new behaviors in polygon transformations under iteration.

Findings

Identification of area-expanding and area-contracting regions

Characterization of the map's iterative behavior on polygons

Insights into the topological structure of the transformation

Abstract

Using experimental techniques, we study properties of the "circumcenter map", which, upon $n$ iterations sends an $n$-gon to a scaled and rotated copy of itself. We also explore the topology of area-expanding and area-contracting regions induced by this map.