The structure factor of fat deterministic Vicsek fractals: a small-angle scattering study

TL;DR

This paper investigates the small-angle scattering structure factor of fat deterministic Vicsek fractals, revealing their self-similarity and scattering properties, and introduces a method to analyze their scattering behavior.

Contribution

It introduces deterministic fattened Vicsek fractals and calculates their structure factors, demonstrating self-similarity in scattering properties across iteration ranges.

Findings

Fat fractals are self-similar within certain iteration ranges.

The structure factor of fat fractals can be explicitly calculated.

Scattering properties of fat fractals resemble those of regular fractals within specific scales.

Abstract

We study here the small-angle scattering structure factor for deterministic fat fractals in the reciprocal space. It is shown that fat fractals are exact self-similar in the range of iterations having the same values of the scaling factor, and therefore in each of these ranges all the properties of regular fractals can be inferred to fat fractals. In order to illustrate the above findings we introduce deterministic fattened versions of Vicsek deterministic fractals. We calculate the mono- and polydisperse structure factor and study its scattering properties.