Analysis of the convex hull of the attractor of an IFS

TL;DR

This paper introduces a method to analyze the convex hulls of IFS attractors using a directional width function, enabling efficient geometric property computations and analysis.

Contribution

It presents a novel approach to analyze IFS attractors' convex hulls through a directional width function and self-similarity equations.

Findings

Method allows quick distance checks from the convex hull

Enables analytical computation of convex hull area

Facilitates boundary length analysis

Abstract

In this paper we will introduce the methodology of analysis of the convex hull of the attractors of iterated functional systems (IFS) - compact fixed sets of self-similarity mapping. The method is based on a function which for a direction, gives width in that direction. We can write the self similarity equation in terms of this function, solve and analyze them. Using this function we can quickly check if the distance from K of a given x is smaller than a given distance or even compute analytically convex hull area and the length of its boundary