A geometric iterated function system on triangles

TL;DR

This paper introduces a geometric iterated function system on the space of ordered triangles, demonstrating convergence despite containing a non-contraction map, with functions having clear geometric interpretations.

Contribution

It constructs a novel iterated function system on triangle moduli space that converges even with a non-contraction component, linking geometric meaning to the functions.

Findings

The system converges on the moduli space of triangles.

Functions involved have meaningful geometric interpretations.

Includes a non-contraction map within the system.

Abstract

We construct a converging geometric iterated function system on the moduli space of ordered triangles, for which the involved functions have geometric meanings and contain a non-contraction map under the natural metric.