Fractal Interpolation Function On Products of the Sierpi\'nski Gaskets

TL;DR

This paper constructs fractal interpolation functions on the product of two Sierpiński gaskets, analyzes their smoothness, and estimates their fractal dimensions, advancing understanding of fractal functions on complex fractal sets.

Contribution

It introduces a method to build FIFs on product fractals and studies their smoothness and fractal dimension, which is a novel extension in fractal analysis.

Findings

FIFs are Hölder continuous under certain conditions

Bounds on the fractal dimension of FIFs are established

Results contribute to the theory of fractal functions on product fractals

Abstract

In this paper, we aim to construct fractal interpolation function(FIF) on the product of two Sierpi\'nski gaskets. Further, we collect some results regarding smoothness of the constructed FIF. We prove, in particular, that the FIF are H\"older functions under specific conditions. In the final section, we obtain some bounds on the fractal dimension of FIF.