Drip paintings and fractal analysis

Katherine Jones-Smith, Harsh Mathur, and Lawrence M. Krauss
Phys. Rev. E 79, 046111 – Published 30 April 2009

Abstract

It has been claimed that fractal analysis can be applied to unambiguously characterize works of art such as the drip paintings of Jackson Pollock. This academic issue has become of more general interest following the recent discovery of a cache of disputed Pollock paintings. We definitively demonstrate here, by analyzing paintings by Pollock and others, that fractal criteria provide no information about artistic authenticity. This work has led us to a result in fractal analysis of more general scientific significance: we show that the statistics of the “covering staircase” (closely related to the box-counting staircase) provide a way to characterize geometry and distinguish fractals from Euclidean objects. Finally we present a discussion of the composite of two fractals, a problem that was first investigated by Muzy. We show that the composite is not generally scale invariant and that it exhibits complex multifractal scaling in the small distance asymptotic limit.

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  • Received 24 October 2007

DOI:https://doi.org/10.1103/PhysRevE.79.046111

©2009 American Physical Society

Authors & Affiliations

Katherine Jones-Smith1, Harsh Mathur1, and Lawrence M. Krauss2

  • 1Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106-7079, USA
  • 2School of Earth and Space Exploration, Department of Physics and Beyond Center, Arizona State University, P.O. Box 871404, Tempe, Arizona 85287-1404, USA

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Vol. 79, Iss. 4 — April 2009

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The editors of Physical Review E are pleased to announce that the journal’s stated scope has been expanded to explicitly include the term “Biological Physics.”

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