Multifractal analysis of a class of self-affine Moran sets

TL;DR

This paper studies the detailed multifractal spectrum of specific self-affine Moran sets, deriving a formula for the spectrum under certain separation conditions, advancing understanding of their fractal properties.

Contribution

It provides a new formula for the multifractal spectrum of self-affine Moran sets with fixed frequencies, under separation conditions, extending previous theoretical results.

Findings

Derived the formula for the multifractal spectrum $H(\alpha)$

Established conditions under which the formula holds

Enhanced understanding of the fractal structure of Moran sets

Abstract

In the paper, we investigate the fine multifractal spectrum of a class of self-affine Moran sets with fixed frequencies, and we prove that under certain separation conditions, the fine multifractal spectrum $H(\alpha)$ is given by the formula $$ H(\alpha)=\inf_{-\infty<t<+\infty} \{\alpha t+\beta(t)\}. $$