Study of attractors and fractal functions on the product spaces and Dimensional aspects

TL;DR

This paper investigates the properties of attractors and fractal functions in product spaces, focusing on Hausdorff metrics, attractor relations, and dimensional bounds, contributing to the understanding of fractal geometry in higher dimensions.

Contribution

It introduces a new framework for analyzing attractors and fractal functions on product spaces, including establishing metric equivalences and dimension bounds.

Findings

Equivalence between product Hausdorff metric and Hausdorff metric on the product space.

Relations between attractors of product IFS and coordinate IFSs.

Dimension bounds for homogeneous and inhomogeneous attractors.

Abstract

In this paper, the product of the Hausdorff metric on the product space is defined and the equivalency between the product Hausdorff metric and the Hausdorff metric on the product space is established. The finite product of the iterated function systems (IFS) on the product space is considered and the relation between the attractor of the product IFS and the attractors of the co-ordinate IFSs is studied. Dimension bounds of the homogeneous and inhomogeneous attractors on the product space is established. Also, the product fractal interpolation function on the higher dimensional space is constructed.