Describing abstract art in words is challenging, but a new analytical method based on two-dimensional multifractal tools provides an objective approach. Developed by a team from the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ PAN), the University of Rzeszow, and the Cracow University of Technology, this method has been detailed in the journal Chaos. Researchers demonstrated the method's utility by analyzing Mars' surface, the Crab Nebula, and Pollock's art.
"Multifractal analyses, even in one-dimensional cases, are computationally complex and demand expertise. Our work offers a complete, practical computational algorithm for detecting hierarchical multifractal organization in two-dimensional planes. This includes identifying directional asymmetry and analyzing its features," said Prof. Stanislaw Drozdz of IFJ PAN and PK.
The method resembles tomography, starting with a point on the surface, often at the edge or corner. The surface is scanned at successive angles within strips of varying widths, typically three. Within each strip, multifractal components and their variability are calculated. This ensures full coverage of the area and precise determination of the multifractal spectrum.
"Although scanning successive directions is conceptually simple, practical implementation is intricate. Mishandling detected multifractal dependencies can reduce the output to mere noise, erasing meaningful results," explained Prof. Rafal Rak, lead author of the study.
To validate the technique, researchers analyzed two astronomical images. The Mars Global Surveyor captured wind-eroded, parallel depressions on Mars' surface, showing clear linear directionality. The Crab Nebula, a supernova remnant, revealed natural radial patterns. The resulting multifractal spectra accurately reflected these dominant features, with the Mars image showing a single minimum in its spectrum and the Crab Nebula revealing a richer, asymmetrical structure.
The method was then applied to Pollock's paintings. Researchers studied three works marking key phases of his career: "Mural" (1943), "Lavender Mist" (1950), and "Convergence" (1952). The multifractal analysis showed that "Mural" had the most developed multifractal spectrum with significant directional variability and right-sided asymmetry, indicating detailed craftsmanship. "Lavender Mist" displayed an almost flat spectrum, suggesting diminished multifractality and directionality. "Convergence" combined elements of both earlier works, with a spectrum showing subtle right-sided asymmetry.
"Until now, assessing abstract paintings was subjective and imprecise. Our multifractal formalism offers a more objective classification tool," said Prof. Drozdz. He added, "This method could also help verify the authenticity of paintings, identify artists, classify workshops, and even appraise art value."
The practicality of the method is notable; calculations can run on standard computers within hours. While this study presented the tool's statistical foundations, the researchers aim to enhance and expand its applications.
Research Report:Quantifying multifractal anisotropy in two dimensional objects
Related Links
Institute of Nuclear Physics
Understanding Time and Space
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