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Published on: August 30, 2013
Drip paintings and fractal analysis
Katherine Jones-Smith1, Harsh Mathur, Lawrence M Krauss
1Department of Physics, Case Western Reserve University, Cleveland, Ohio 44106-7079, USA.
Summary
Fractal analysis cannot determine the authenticity of Jackson Pollock paintings. New fractal statistics can, however, distinguish complex geometries and fractals from Euclidean objects.
Area of Science:
- Fractal Geometry
- Art Authentication
- Complex Systems
Background:
- Fractal analysis has been proposed as a method to authenticate artworks, particularly the drip paintings attributed to Jackson Pollock.
- The debate over authenticity has intensified with the discovery of disputed Pollock paintings, necessitating rigorous analytical methods.
Purpose of the Study:
- To investigate the efficacy of fractal criteria in determining the artistic authenticity of paintings.
- To develop novel fractal analysis techniques for characterizing geometric complexity and distinguishing between fractal and Euclidean objects.
- To explore the scaling properties of composite fractal systems.
Main Methods:
- Analysis of fractal dimensions of paintings by Jackson Pollock and other artists.
- Development and application of the 'covering staircase' statistics, related to box-counting methods.
- Theoretical investigation of the scaling behavior of composite fractal structures.
Main Results:
- Fractal criteria were found to be insufficient for unambiguously characterizing artistic authenticity in paintings.
- The 'covering staircase' statistics effectively characterize geometry and differentiate fractals from Euclidean objects.
- Composite fractal systems were shown to be not generally scale invariant and exhibit complex multifractal scaling.
Conclusions:
- Fractal analysis is not a reliable tool for art authentication.
- Novel fractal statistics offer a robust method for geometric characterization and classification.
- The study advances the understanding of multifractal scaling in composite systems.
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