Construction and Box-counting Dimension of the Edelstein Hidden Variable Fractal Interpolation Function

TL;DR

This paper develops a new class of fractal interpolation functions using Edelstein contractions, analyzes their smoothness, and estimates the box-counting dimension of their graphs, contributing to fractal geometry and interpolation theory.

Contribution

It introduces a novel construction of hidden variable fractal interpolation functions with Edelstein contractions and provides bounds on their fractal dimension.

Findings

Constructed a new class of fractal interpolation functions.

Established an upper bound for the box-counting dimension.

Analyzed the smoothness properties of the functions.

Abstract

This paper presents the construction of a hidden variable fractal interpolation function using Edelstein contractions in an iterated function system based on a finite collection of data points. The approach incorporates an iterated function system where variable functions act as vertical scaling factors leading to a generalised vector-valued fractal interpolation function. Furthermore, the paper rigorously examines the smoothness of the constructed function and establishes an upper bound for the box-counting dimension of its graph.