Topological conditions on inhomogeneous fractals in Martin boundary theory and their algorithmic testing

TL;DR

This paper explores applying Martin boundary theory to inhomogeneous fractals, simplifies the conditions needed, and develops an algorithm to verify these conditions on fractal attractors.

Contribution

It introduces a simplified condition for Martin boundary theory on fractals and presents a new algorithm for verifying this condition computationally.

Findings

Simplified the condition for applying Martin boundary theory to inhomogeneous fractals.

Developed a computer algorithm to check if a fractal attractor meets the condition.

Facilitated easier verification of fractal properties relevant to boundary theory.

Abstract

We want to consider Martin boundary theory applied to inhomogeneous fractals. This is under some conditions possible, but up to now it is not clear, how one can easily check, if a certain fractal fulfills those conditions. We want to simplify one condition and further develop a computer algorithm, which can check, if an attractor fulfills the condition.