Quantifying multifractal anisotropy in two dimensional objects

TL;DR

This paper introduces a new 2D multifractal analysis method to quantify anisotropy in surfaces and images, revealing directional multifractality and evolution of artistic works.

Contribution

It presents an efficient, direction-sensitive extension of MFDFA for 2D data, applicable to natural surfaces, astronomical images, and artworks.

Findings

Detected previously unknown directional multifractality in Martian surface and Crab Nebula data.

Analyzed Jackson Pollock paintings, showing evolution of multifractal properties over time.

Validated method on synthetic structures, confirming effectiveness and consistency.

Abstract

An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis (MFDFA) into 2D. It is tested on synthetic structures to ensure its effectiveness, with results indicating consistency. The interdisciplinary potential of this method in describing real surfaces and images is demonstrated, revealing previously unknown directional multifractality in data sets from the Martian surface and the Crab Nebula. The multifractal characteristics of Jackson Pollock's paintings are also analyzed. The results point to their evolution over the time of creation of these works.