Conductivity properties of the Sierpinski triangle

TL;DR

This paper investigates the electrical conductivity properties of the fractal Sierpinski triangle, deriving asymptotic critical exponents and dimensions as the correlation length approaches infinity.

Contribution

It provides the first asymptotic analysis of conductivity in the multifractal Sierpinski triangle, linking fractal geometry with electrical properties.

Findings

Critical exponents for conductivity are derived asymptotically.

Dimensions related to conductivity are obtained in the limit of infinite correlation length.

The study enhances understanding of transport properties in fractal structures.

Abstract

The classic Sierpinski triangle comprised of conducting bonds is multifractal. Thus the critical exponents and dimensions related to the conductivity are obtained asymptotically--that is, in the limit that the correlation length {\xi} of the recursive triangle goes to infinity.