Dimensional analysis of fractal interpolation functions

TL;DR

This paper rigorously analyzes the dimensions of fractal interpolation functions, especially estimating the box dimension of alpha-fractal functions, based on their defining parameters and structure.

Contribution

It provides an exact estimation method for the box dimension of alpha-fractal functions, advancing the understanding of their geometric complexity.

Findings

Exact estimation of box dimension for alpha-fractal functions

Analysis of fractal interpolation functions on bounded intervals

Relationship between function parameters and fractal dimensions

Abstract

We provide a rigorous study on dimensions of fractal interpolation function defined on a closed and bounded interval of $\mathbb{R}$ which is associated to a continuous function with respect to a base function, scaling functions and a partition of the interval. In particular, we provide an exact estimation of the box dimension of $\alpha$-fractal functions.