Anisotropy and percolation threshold in a multifractal support

TL;DR

This paper investigates how anisotropy and the structure of a multifractal support influence the percolation threshold, revealing a relationship between occupation probability, neighbor count, and anisotropy.

Contribution

It introduces a study of percolation on a multifractal object, analyzing how anisotropy affects the percolation threshold and neighbor interactions.

Findings

Percolation threshold $p_c$ depends on anisotropy parameter $ ho$.

The average number of neighbors influences $p_c$.

Anisotropy significantly affects percolation properties.

Abstract

Recently a multifractal object, $Q_{mf}$, was proposed to study percolation properties in a multifractal support. The area and the number of neighbors of the blocks of $Q_{mf}$ show a non-trivial behavior. The value of the probability of occupation at the percolation threshold, $p_{c}$, is a function of $\rho$, a parameter of $Q_{mf}$ which is related to its anisotropy. We investigate the relation between $p_{c}$ and the average number of neighbors of the blocks as well as the anisotropy of $Q_{mf}$.