An Explicit Formula of the Intrinsic Metric on the Sierpinski Gasket via Code Representation

TL;DR

This paper provides an explicit formula for the intrinsic metric on the Sierpinski Gasket using code representations, filling a gap in the existing literature which lacked such a formula.

Contribution

The paper introduces a novel explicit formula for the intrinsic metric on the Sierpinski Gasket based on code representations of its points.

Findings

Explicit formula for the intrinsic metric derived

Utilizes code space representation for the Sierpinski Gasket

Advances understanding of geometric properties of fractals

Abstract

The computation of the distance between any two points of the Sierpinski Gasket with respect to the intrinsic metric has already been investigated by several authors. In the literature there is not an explicit formula using the code space of the Sierpinski Gasket. In this paper, we give an explicit formula for the intrinsic metric on the Sierpinski Gasket via code representations of its points.