|Ivars Peterson's MathTrek|
September 20, 1999
Pollock's signature technique, which he developed in the late 1940s and early 1950s, was to drip house paint--in colors such as black, white, silver, taupe, and teal--from hardened, worn-out brushes, sticks, and other applicators onto enormous sheets of canvas spread across the floor. His approach, however, was somewhat more systematic than the chaotic results might suggest.
Pollock would begin by using a series of fluid strokes to draw a collection of loopy figures. When the paint dried, he would connect the scattered shapes with darker, thicker slashes of pigment. Additional layers of dripped, poured, and hurled paint would further obscure the original forms, creating a dense web of trails across the canvas.
Physicist Richard P. Taylor of the University of New South Wales in Sydney, Australia, who is also trained as an artist, has taken a mathematical look at Pollock's splatter paintings to try to uncover the secret of their appeal to many viewers.
"The unique thing about Jackson Pollock was that he abandoned using the brush on canvas and actually dripped the paint," Taylor says. "That produced trajectories of paint on the canvas that were like a [two-dimensional] map or fingerprint of his [three-dimensional] motions around the canvas."
Taylor photographed the Pollock painting Blue Poles, Number 11, 1952 (see http://www.kn.pacbell.com/wired/art/pollock.html), which the Australian government had purchased in 1972 for $2 million and put on display at the National Gallery of Australia in Canberra. He and his colleagues then scanned the photos and used a computer to analyze the color schemes and trajectories evident in the painting.
The researchers discovered that Pollock's patterns could be characterized as fractals--shapes that repeat themselves on different scales within the same object. In a fractal object or pattern, each smaller structure is a miniature, though not necessarily identical, version of the larger form. Fractals often occur in nature, from the meanderings of a coastline, in which the shapes of small inlets approximate the curves of an entire shoreline, to the branchings of trees and the lacy forms of snowflakes and ferns.
A fractal pattern, whether in nature or in a Pollock painting, is subconciously pleasing, Taylor suggests.
In the June 3 Nature, Taylor and his colleagues present the results an analysis of paintings that Pollock made between 1943 and 1952. They quantified the fractal content of the paintings and calculated a fractal dimension for each one.
"Our analysis of a film of Pollock while painting shows that the fractal patterns occurring over the lower range [of size scales] are determined by the dripping process, whereas the fractal patterns across the higher range are shaped by his motions around the canvas," the team reports.
The analysis suggests that Pollock refined his dripping technique over the years. The fractal dimension increases from about 1 (sparse, simple) in 1943 to 1.72 (thickly layered, complex) in 1952. His 1947 painting Alchemy (see http://www2.iinet.com/art/20th/american/pollock/pollck42.jpg), for example, has a fractal dimension close to 1.5.
"The fractal analysis could be used as a quantitative, objective technique to validate and date Pollock's drip paintings," the researchers conclude. "The change in [fractal dimension] reflects a dramatic evolution in visual character."
Copyright 1999 by Ivars Peterson
Mandelbrot, B.B. 1983. The Fractal Geometry of Nature. New York: W.H. Freeman.
Peterson, I., and N. Henderon. In press. Math Trek: Adventures in the MathZone. New York: Wiley.
Tuchman, P. Jackson Pollock: Modernism's shooting star. Smithsonian 29(November):96.
Taylor, R. 1998. Splashdown. New Scientist (July 25):30.
Taylor, R.P., A.P. Micolich, and D. Jones. 1999. Fractal analysis of Pollock's drip paintings. Nature 399(June 3):422.
Additional information about Pollock's life and painting techniques is available at http://www.moma.org/exhibitions/pollock/website100/index.html.
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