Never mind the Pollock ‘fractals’

Scientists strengthen claim that fractal analysis for authenticating a Pollock painting is moot

PITTSBURGH — A proposed method for authenticating artist Jackson Pollock’s drip paintings does not hold up under scrutiny, a new analysis finds.

What’s more, the analysis uncovered a new way to identify a mathematical fractal, Katherine Jones-Smith of Case Western Reserve University in Cleveland reported March 19 at a meeting of the American Physical Society.

A cache of 32 paintings discovered in 2003 — claimed by some to be authentic Pollocks — sparked a controversy among art historians and soon brought physicists into the quagmire in an effort to identify the paintings’ origins.

A paper published in Nature in 1999 by Richard Taylor of the University of Oregon in Eugene claimed that authentic Pollock paintings were fractal, a mathematical property in which patterns are similar across many scales, like a coastline, which has the same overall shape over very short or very large segments. A true fractal displays this self-similarity over an infinite range. If Pollock paintings were all fractal, as Taylor suggested, then fractal analysis might confirm the authenticity of paintings in the cache. This original fractal analysis judged that none of six disputed Pollock paintings were fractal, and thus, not authentic.

In a brief response published in Nature in 2006, Jones-Smith and her colleagues argued that the analysis was flawed. The centerpiece of the claim was a crude drawing of stars made by Jones-Smith. According to fractal analysis, Jones-Smith’s childish drawing was an authentic Pollock painting. Although an algorithm may think the star drawing was an authentic Pollock, says Jones-Smith, no art historian would be so easily fooled.

In the new research, Jones-Smith and colleagues commissioned local painters to create drip paintings in the size and style of Pollock. The researchers applied fractal analyses to two such paintings, and three undisputed Pollock paintings. Both of the two commissioned drip paintings turned out to be fractal, and thus, appeared to be authentic Pollocks. Meanwhile, only one of three undisputed Pollocks was fractal.

“That closes the question,” says Jones-Smith, that fractal analyses cannot be used to authenticate the origins of these paintings. Taylor’s work was “well-motivated, but when it comes right down to it, it doesn’t stand up under scrutiny” Jones-Smith says. “When science does come into these interplays, it should be done with caution, with rigor, with error bars.”

This example of a faulty method underscores that caution is needed when interpreting scientific results, especially when applied to the art world, Peter Lu of Harvard University said at a news briefing March 18 at the APS meeting. “It’s a little dangerous for scientists to get too far into the business of providing the final word. I think it’s a little more complicated than that.”

In the course of invalidating the fractal validation method, the researchers did obtain some positive mathematical findings. “The results were motivated by drip paintings, but we found out something about mathematics,” says Jones-Smith.

A common way to identify fractals in two-dimensional objects, like paintings, is to use a technique called box counting, in which a computer program draws boxes of all different sizes around the objects in the paintings, and identifies how many boxes are filled. Plotting the box sizes against the number of filled boxes gives an almost straight line. If the slope of a straight line drawn to fit the data is not an integer, the object is a fractal.

In their new study, Jones-Smith and her colleagues found that whatever the slope, individual fractal objects deviate from the straight line in a different and more complex way than non-fractal objects. This deviation can be used to distinguish a fractal from a normal object, the researchers write in a paper to appear in Physical Review E.

The new fractal identification method has yet to be tested in other systems. “Is this useful or not? We don’t yet know,” says Harsh Mathur, Jones-Smith’s collaborator at Case Western Reserve.

Scientists strengthen claim that fractal analysis for authenticating a Pollock painting is moot.
Physicists found that two commissioned drip paintings like the one shown here are fractal objects, indicating that fractal analysis is not a reliable marker of an authentic Jackson Pollock painting.  Alexandra Ash and Michael Hallen

Laura Sanders is the neuroscience writer. She holds a Ph.D. in molecular biology from the University of Southern California.

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