Valuation theory, generalized IFS attractors and fractals

TL;DR

This paper explores how valuation rings and valued fields can be used to generalize the concepts of topological IFS attractors and fractal spaces, broadening their applicability.

Contribution

It introduces a framework for extending fractal and attractor notions to valuation-based structures, expanding the theoretical understanding of fractals.

Findings

Valuation rings can serve as models for generalized fractal spaces.

The notions of IFS attractors can be adapted to valuation-theoretic contexts.

The paper provides a foundation for further exploration of fractals in algebraic structures.

Abstract

Using valuation rings and valued fields as examples, we discuss in which ways the notions of "topological IFS attractor" and "fractal space" can be generalized to cover more general settings.