Box dimension of fractal functions on attractors

TL;DR

This paper investigates the box dimension of a broad class of fractal interpolation functions defined on attractors, providing bounds and exact values in more general settings than previously studied.

Contribution

It extends the analysis of fractal function dimensions to non-affine maps, variable scale vectors, and general attractors, including the Sierpinski Gasket.

Findings

Derived bounds for fractal function dimensions.

Calculated exact box dimension for non-affine functions on specific fractals.

Generalized previous results to broader classes of attractors and maps.

Abstract

We study a wide class of fractal interpolation functions in a single platform by considering the domains of these functions as general attractors. We obtain lower and upper bounds of the box dimension of these functions in a more general setup where the interpolation points need not be equally spaced, the scale vectors can be variables and the maps in the corresponding IFS can be non-affine. In particular, we obtain the exact value of the box dimension of non-affine fractal functions on general m-dimensional cubes and Sierpinski Gasket.