Box-counting dimension of a kind of fractal interpolation surface on rectangular grids

TL;DR

This paper estimates the Box-counting dimension of fractal surfaces generated by iterated function systems with variable contraction factors on rectangular grids, effectively modeling complex natural surfaces.

Contribution

It introduces a method to compute the Box-counting dimension of fractal interpolation surfaces with variable contraction factors on arbitrary data sets.

Findings

Provides a formula for the Box-counting dimension of these fractal surfaces

Applicable to modeling complex natural surfaces

Enhances understanding of fractal surface geometry

Abstract

We estimate a Box-counting dimension of fractal surfaces which are generated by iterated function systems with a vertical contraction factor function on an arbitrary data set over rectangular grids and can express well a lot of natural surfaces with very complicated structures.