Math in the News
Fractal Analysis Apparently Fails an Art Authentication Test
November 27, 2007
A new study has raised doubts about using the mathematics of fractals to distinguish genuine Jackson Pollock drip paintings from fakes. That's because similar complex geometric patterns apparently turn up in splatter paintings created by amateurs.
Eight years ago, physicist Richard Taylor, now at the University of Oregon, reported that Pollock's paintings contain distinctive splatters within splatters. He attributed the patterns to the artist's method: swaying over a canvas while dribbling paint from brushes, sticks, and straight from paint cans. After 32 previously unknown Pollock paintings turned up in 2003, the PollockKrasner Foundation last year commissioned Taylor to authenticate six of them by using fractal clues.
However, physicists Katherine JonesSmith and Harsh Mathur, both from Case Western Reserve University, reported last year in Nature that they uncovered fractal signatures in mere sketches of different-size stars and circles that match Pollock's. JonesSmith had drawn the images while preparing a presentation on Taylor's work, which she initially believed was correct. The revelation that her images and Pollock's paintings contain apparently identical fractal patterns caused Mathur to rethink his stance. "Fractal analysis doesn't allow you to have a position" on the authenticity of a Pollock painting, he told Scientific American.
More recently, Jones-Smith, Mathur, and Lawrence Krauss analyzed three drip paintings known to be created by Pollock but not originally analyzed by Taylor. They found that none of the Pollock paintings met stringent criteria to qualify as fractal in form. Their new findings are in a report submitted to Physical Review Letters.
Taylor's counterargument is that the researchers applied his fractal criteria incorrectly on one of Pollock's works and noted that their analysis of another hinges on paint covering less than 5 percent of the canvas. Moreover, he said, "there's an image out there of fractal analysis where you send the image through a computer and if a red light comes on it means it isn't a Pollock and if a green light comes on it is. We have never supported or encouraged such a mindless view."
Even if the new results are correct, computer scientist Hany Farid of Dartmouth College noted, fractal analysis is only one method in the field of authentication, which includes historical and aesthetic judgment. "None of these tools stands by itself," he concluded.