Lacunarity of Random Fractals

TL;DR

This paper introduces a set of universal and non-universal properties of random fractals using generalized singularity spectra and energy integral generalizations, enhancing understanding of their complex structures.

Contribution

It presents a novel framework combining generalized singularity spectra and energy integrals to analyze the properties of random fractals.

Findings

Characterization of universal properties via generalized singularity spectra

Recovery of non-universal properties through energy integral generalizations

Extension of multifractal analysis to complex analogs

Abstract

We discuss properties of random fractals by means of a set of numbers that characterize their universal properties. This set is the generalized singularity specturm that consists of the usual spectrum of mulitfractal dimensions and the associated complex analogs. Furthermore, non-universal properties are recovered from the study of a series of functions which are generalizations of the so-called energy intergral.