http://www.sciam.com/article.cfm?chanID=sa003&articleID=F772E600-E7F2-99DF-31C002B3A0D3AFF2
ScientificAmerican.com
October 31, 2007
Pollock or Not? Can Fractals Spot a Fake Masterpiece?
Complex geometric patterns turn up in non-Pollock drip paintings
A new study attacks the technique of using fractals, the repeating
patterns found in everything from coastlines to fern fronds, to help
distinguish authentic Jackson Pollock drip paintings from paint
splattered by lesser hands.
In a paper submitted for publication to a major physics journal,
researchers report that previously published criteria for identifying
genuine Pollocks based on the presence of fractals—patterns that recur
in varying sizes like Russian dolls nested inside one another—would
wrongly grant Pollock status to a pair of amateur drip paintings.
Some researchers, however, are skeptical that the new method faithfully
replicates that of University of Oregon physicist Richard Taylor, who
first reported eight years ago that five Pollock paintings contained
distinctive splatters within splatters, which he has attributed to the
way "Jack the Dripper" swayed over the canvas while dribbling paint from
brushes, sticks or straight from the can.
The Pollock–Krasner Foundation, which represents the estates of Pollock
and his wife Lee Krasner, commissioned Taylor last year to examine six
of 32 alleged Pollock drip paintings for fractal clues as to whether the
master dripper (dead since 1956) had truly created them; the paintings,
discovered in 2003, turned up fractalless.
Upon learning the news, physicists Katherine Jones–Smith and Harsh
Mathur of Case Western Reserve University in Cleveland, Ohio, published
their own Nature paper reporting the discovery of a similar fractal
signature in quick sketches of different size stars or circles.
Jones–Smith had drawn the images two years earlier while preparing a
presentation on Taylor's work, which she initially believed was correct.
Much to her surprise, she discovered that her unsophisticated images
contained seemingly identical fractal patterns.
To rebut the obvious counterargument—that stars look nothing like drip
paintings—she, Mathur and Case Western cosmologist Lawrence Krauss have
now analyzed three known Pollock drip paintings that Taylor had not
examined in detail: Free Form (1946), Untitled (circa 1950) and Wooden
Horse: Number 10A, 1948.
After using one of two separate computer techniques to isolate splatter
marks of different colors, the researchers scanned for fractals in each
layer of color by digitally counting colored pixels (or boxes) of
various sizes. In this type of fractal, the number of boxes of each size
relates to the box size raised to a power that holds constant over a
range of sizes.
None of the Pollocks met stringent fractal criteria, although Free Form
did satisfy what they consider a loose definition of a fractal and
Wooden House failed its test in only two of six colors, they report in
their paper submitted to Physical Review Letters, which has yet to be
reviewed by other scientists.
Further complicating matters, the researchers identified fractals in two
drip paintings created for the study by students [see image above]. They
next examined two of the alleged Pollocks studied by Taylor, one of
which, chosen for its resemblance to Free Form, passed the loose fractal
test, whereas the other, resembling Wooden Horse, failed the test.
The new results clash with a 2006 Pattern Recognition Letters paper in
which Taylor and colleagues reported identifying an identical fractal
pattern in 14 known Pollocks but not among 37 drip paintings by
University of Oregon undergraduates or 14 paintings of unknown origin
thought to date to Pollock's era.
"Our position," Mathur says, "is that fractal analysis doesn't allow you
to have a position" on the authenticity of a Pollock.
Hany Farid, a professor of computer science at Dartmouth College in New
Hampshire who has followed the debate, says he sees flaws in the new
study. "I think they took a fairly simplistic way of separating those
colors," which he says could have skewed their results.
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Taylor argues that the researchers applied his fractal criteria
incorrectly on Untitled and notes that their Wooden Horse analysis
hinges on paint covering less than 5 percent of the canvas, which makes
drawing conclusions tricky.
Moreover, he says, the group's conclusion turns on a misconception.
"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, Farid says, fractal analysis can
still serve as one piece of evidence in the broader puzzle of
authentication, which also involves historical and aesthetic judgments.
Earlier this year, for example, a Harvard team reported that two
pigments found in the 32 alleged Pollocks were not used in paints before
1996 and 1971.
"None of these tools stands by itself," Farid says.
Owners of authentic Pollocks, however, do stand to make a lot of money.
Last year, the Pollock painting No. 5, 1948, was reportedly sold to a
Mexican financier for a record $140 million.
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