'Order in Pollock's Chaos'

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Computer analysis is helping to explain the appeal of Jackson Pollock’s paintings. The artist’s famous Order drips and swirls create fractal patterns, similar to those formed in nature by trees, clouds and coastlines in Pollock’s By Richard P. Taylor Chaos n a drunken, suicidal state on a stormy March night, Jack- BLUE POLES: NUMBER 11, 1952 (enamel and aluminum paint on canvas, 210 son Pollock (1912–1956) laid down the foundations of cm by 486.8 cm) exemplifies Pollock’s trademark interweaving swirls of his masterpiece Blue Poles: Number 11, 1952. He un- paint, which evolved through a series of depositions over the course of making a painting, a period of six months in the case of Blue Poles. rolled a large canvas across the ﬂoor of his windswept Ibarn and, using a wooden stick, dripped the canvas with house- full-time. I left the physics department of the University of New hold paint from an old can. South Wales and headed off to the Manchester School of Art This was not the ﬁrst time the artist had dripped a painting in England, which had a reputation for a “sink or swim” ap- onto canvas. In contrast to the broken lines painted by conven- proach to painting. In the bleak month of February, the school tional brush contact, Pollock had developed a technique in which packed us students off to the Yorkshire moors in the north of he poured a constant stream of paint onto horizontal canvases England, telling us that we had one week to paint what we saw. to produce uniquely continuous trajectories. This deceptively But a violent snowstorm made the task impossible, so I sat down simple act polarized opinion in the art world. Was this primitive with a few friends, and we came up with the idea of making na- painting style driven by raw genius, or was he simply a drunk ture paint for us. who mocked artistic traditions? To do this, we assembled a huge structure out of tree branch- I had always been intrigued by Pollock’s work because, in es blown down by the storm. One part of the structure acted like addition to my life as a physicist, I painted abstract art. Then, a giant sail, catching the motions of the wind swirling around it.

NATIONAL GALLERY OF AUSTRALIA, CANBERRA, ©2002 POLLOCK- KRASNER FOUNDATION/ARTISTS RIGHTS SOCIETY (ARS), NEW YORK in 1994, I decided to put my scientiﬁc career on hold and to paint This motion was then transferred to another part of the struc-

www.sciam.com SCIENTIFIC AMERICAN 117 ture that held paint containers, and these examine how natural systems, such as the D, which quantifies the scaling relation dripped a pattern corresponding to the weather, change with time. They found among the patterns observed at different wind’s trajectory onto a canvas on the that these systems are not haphazard; in- magnifications. For Euclidean shapes, di- ground. As another large storm began to stead, lurking underneath is a remarkably mension is a simple concept described by move through, we decided to retreat in- subtle form of order. They labeled this be- the familiar integer values. For a smooth doors, leaving the structure to paint havior “chaotic,” and a new scientific line (containing no fractal structure), D through the night. The next day the storm field called chaos theory grew up to ex- has a value of 1; for a completely filled had passed—and the image it left behind plain nature’s dynamics. Then, in the area, its value is 2. For a fractal pattern, looked like a Pollock! 1970s, a new form of geometry emerged however, the repeating structure causes Suddenly, the secrets of Jackson Pol- to describe the patterns that these chaot- the line to occupy area. D then lies in the lock seemed to fall into place for me: he ic processes left behind. Given the name range between 1 and 2; as the complexi- must have adopted nature’s rhythms “fractals” by their discoverer, Benoit ty and richness of the repeating structure when he painted. At this point, I realized Mandelbrot, the new forms looked noth- increase, its value moves closer to 2. I would have to head back into science to ing like traditional Euclidean shapes. In To figure out how all this might apply determine whether I could identify tangi- contrast to the smoothness of artificial to Pollock’s paintings, I went back to my ble traces of those rhythms in his artwork. lines, fractals consist of patterns that re- lab at New South Wales, where I turned cur on finer and finer magnifications, to the computer for help in quantifying the Art Anticipates Science building up shapes of immense complex- patterns on his canvases. It would have DURING POLLOCK’S ERA, nature was ity. The paintings created by our branch been impossible to perform this kind of assumed to be disordered, operating es- contraption suggested to me that the analysis without the precision and com- sentially randomly. Since that time, how- seemingly random swirls in Pollock’s putational power provided by such equip- ever, two fascinating areas of study have paintings might also possess some subtle ment. So I enlisted two colleagues who emerged to yield a greater understanding order, that they might in fact be fractals. had special computer expertise—Adam of nature’s rules. A crucial feature in characterizing a Micolich, who was researching fractal During the 1960s, scientists began to fractal pattern is the fractal dimension, or analysis techniques for his doctorate in semiconductor devices, and David Jonas, A Brief History of Fractals an expert in image-processing techniques. We started our investigation by scan- ■ Fractal geometry developed from Benoit Mandelbrot’s studies of complexity in ning a Pollock painting into the comput- the 1960s and 1970s. Mandelbrot coined the term “fractal” from the Latin er [see opposite page]; we then covered it fractus (“broken”) to highlight the fragmented, irregular nature of these forms. with a computer-generated mesh of iden- ■ Fractals display self-similarity—that is, they have a similar appearance at any tical squares. By analyzing which squares magnification. A small part of the structure looks very much like the whole. were occupied by the painted pattern and ■ Self-similarity comes in two flavors: exact and statistical. The artificial tree which were empty, we were able to cal- (left series) displays an exact repetition of patterns at different magnifications. culate the statistical qualities of the pat- For the real tree (right), the tern. And by reducing the square size, we patterns don’t repeat exactly; were able to look at the pattern at what instead the statistical amounts to a finer magnification. Our qualities of the patterns analysis examined pattern sizes ranging repeat. Most of nature’s from the smallest speck of paint up to ap- patterns obey statistical proximately a meter. Amazingly, we self-similarity, and so do found the patterns to be fractal. And they Pollock’s paintings. were fractal over the entire size range— ■ Fractals are characterized in the largest pattern more than 1,000 times terms of their “dimension,” or as big as the smallest. Twenty-five years complexity. The dimension is before their discovery in nature, Pollock not an integer, such as the 1, 2 was painting fractals. and 3 dimensions familiar from Euclidean geometry. Instead The Aesthetic Pull fractal dimensions are of Fractals fractional; for example, a TAKING THIS SURPRISING finding a fractal line has a dimension step further, I wondered whether the fractal nature of Pollock’s paintings might between 1 and 2. ARTIFICIAL TREE REAL TREE Exact Self-Similarity Statistical Self-Similarity contribute to their appeal. Only within

the past decade have researchers begun to COURTESY OF RICHARD P. TAYLOR

118 SCIENTIFIC AMERICAN DECEMBER 2002 ANALYZING POLLOCK’S TECHNIQUE

COMPUTER-ASSISTED ANALYSIS of Pollock’s paintings reveals that the artist built up layers of paint in a carefully developed technique that created a dense web of fractals. Pollock was occasionally photographed while painting [see illustration on page 121], which gave me and my colleagues Adam Micolich and David Jonas more insight into his technique.

Autumn Rhythm, 1950, oil on canvas, 266.7 cm by 525.8 cm

We began by scanning a Studying the paintings 1.9 1painting into a computer. We 3chronologically showed could then separate the painting that the complexity of the 1.7

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into its different colored patterns fractal patterns, D, increased D

and analyze the fractal content as Pollock refined his y ( of each pattern. We also looked at D 1.5

technique. One value is plexit the cumulative pattern as the clearly an outlier—1.9 in 1950,

Com layers were added one by one to a work that Pollock later 1.3 build the total picture. A detail destroyed (the analysis is from the black layer of Autumn based on a photograph). He 1.1 Rhythm is shown at the right. may have thought this image 1944 ’46 ’48 ’50 ’52 ’54 was too dense or too complex Year We covered the painting with and subsequently scaled back. a computer-generated mesh 2of identical squares. We then had the computer assess the statistical qualities of the pattern by analyzing which squares are occupied by the pattern (blue) and which are empty (white). D=1 D=1.1 D=1.6 D=1.9 D=2 nonfractal nonfractal Reducing the mesh size (bottom) is equivalent to looking at the The evolution in D value had a smooth, sparse image. If the statistical qualities of patterns a profound effect on the D value is closer to 2, however, at a finer magnification. We appearance of the paintings. the repeating patterns create a found the patterns to be fractal For fractals described by a low shape full of intricate, detailed over the entire size range. D, the repeating patterns build structure.

WHAT EMERGES FROM BOTH the computer analysis and the exam- linking process, the painting’s complexity (its D value) increased over ination of the photographs is evidence of a very systematic, deliberate a timescale of less than a minute. After this rapid activity, Pollock painting process. Pollock started by painting small, localized would take a break. He would then return to the canvas, and over a “islands” of trajectories across the canvas. This is interesting period lasting from two days to six months, he would deposit further because some of nature’s patterns start with small nucleations that layers of different-colored trajectories on top of the black anchor then spread and merge. He next painted longer, extended trajectories layer. Essentially, he was ﬁne-tuning the complexity established by that linked the islands, gradually submerging them in a dense fractal the anchor layer. Even when Pollock had ﬁnished painting, he took web of paint. This stage of the painting formed an anchor layer: it steps that maximized the fractal character, cropping to remove the actually guided the artist’s subsequent painting actions. During the outer regions where the fractal quality deteriorated. —R.P.T.

METROPOLITAN MUSEUM OF ART, NEW YORK, ©2002 POLLOCK-KRASNER FOUNDATION/ARTISTS RIGHTS SOCIETY (ARS), NEW YORK (Autumn Rhythm); COURTESY OF RICHARD P. TAYLOR (computer manipulation of Autumn Rhythm); ALICIA CALLE (graph); PRIVATE COLLECTION, ©2002 POLLOCK-KRASNER FOUNDATION/ARTISTS RIGHTS SOCIETY (ARS), NEW YORK (detail of untitled painting, 1945 [D = 1.1]); KUNSTSAMMLUNG NORDRHEIN-WESTFALEN, DÜSSELDORF, ©2002 POLLOCK-KRASNER FOUNDATION/ARTISTS RIGHTS SOCIETY (ARS), NEW YORK (detail of Number 32, 1950 [D = 1.6]); HANS NAMUTH AND PAUL FALKENBERG, ©MUSEUM OF MODERN ART AND HANS NAMUTH, LTD. (detail of painting from 1950, no longer exists [D = 1.9]) investigate visual preferences for fractal much lower preferred values of 1.3. Al- tion. Working with Branka Spehar of the patterns. Using computer-generated frac- though the discrepancy might indicate University of New South Wales, Colin tals of various D values, Clifford A. Pick- that no D value is preferred over any oth- Clifford, now at the University of Sydney, over of the IBM Thomas J. Watson Re- er—that instead the aesthetic quality of and Ben Newell of University College search Center found that people expressed fractals depends on how the fractals are London, I investigated three fundamental a preference for fractal patterns with a generated—I suspected the existence of a categories of fractals: natural (such as value of 1.8. Then, generating fractals by universally preferred value. trees, mountains and clouds), mathemat- a different computer method, Deborah J. To see whether I was correct, I again ical (computer simulations) and human Aks and Julien C. Sprott of the Universi- sought assistance from experts—this time (cropped sections of Pollock’s paintings). ty of Wisconsin–Madison came up with psychologists who study visual percep- In visual perception tests, participants con-

ALL DRIP PAINTINGS ARE NOT CREATED EQUAL

ARE FRACTALS an inevitable pattern at high magnification consequence of dripping looked very different from paint? No. Consider the drip that at low magnification. A painting at the right, which is Pollock painting (right series), not a Pollock. Working with in contrast, displays the same Ted P. Martin of the University general qualities when viewed of Oregon, I applied our at different magnifications, computer analysis technique regardless of the location and [see box on preceding page] sizes of the segments chosen. to the image, examining its The same magnification complexity at finer and finer sequence was used for both magnifications. We found that paintings. the patterns at different Because the statistical magnifications were not qualities of fractals repeat at described by the same different magnifications, D statistics; in other words, will not change over the they were not fractal. Indeed, various magnifications. It Non-Pollock drip painting, vinyl paint on canvas, 244 cm by 122 cm when the painting was remains constant for the )

magnified, we could see that Pollock painting (red in graph graph the dripped lines quickly ran below), whereas for the non- the painting is not fractal. My to us for analysis was produced out of structure (left series Pollock (yellow), it varies with colleagues and I examine pattern by someone other than Pollock. below). As a consequence, the pattern size, confirming that sizes up to one meter but Fractality, then, offers a concentrate on sizes ranging promising test for authenticating from one to 10 millimeters, a Pollock drip painting. Further, because we have found that this because the D value of the is the most sensitive region for artist’s work rose through the distinguishing between a Pollock years, following a rather and a non-Pollock. predictable trend, the analysis of Number 32, 1950); ALICIA CALLE (

drip paintings sent to us by to date an authentic Pollock detail of collectors who suspected their painting. —R.P.T. acquisitions might have been created by Pollock. Despite superficial similarities with Non-Pollock ), NEW YORK ( shown above ARS Pollock’s work, none of the non-Pollock drip painting

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paintings contained fractal D patterns. The fractals are the Pollock product of the specific technique Pollock devised, and plexity ( all the 20 drip paintings of his Com that we have analyzed have this fractal composition. We could therefore conclude that 0 10 FOUNDATION/ARTISTS RIGHTS SOCIETY ( Non-Pollock drip painting Pollock’s Number 32, 1950 each of the five paintings sent Pattern Size (millimeters) COURTESY OF RICHARD P. TAYLOR (

120 SCIENTIFIC AMERICAN DECEMBER 2002 ); seaweed

POLLOCK, shown above with Lee Krasner in 1950 while at work on One, famously said, “My concern is with the rhythms of nature.” At the right, from top to bottom, are the natural patterns created by seaweed, addressing this possibility, using eye- Pollock’s 1947 painting Full Fathom Five, and the author’s “accidental Pollock,” produced by a windstorm. tracking apparatus to examine the way people look at fractals and at Pollock’s

) sistently expressed a preference for D val- What is the D value of Pollock’s work? paintings. ); COURTESY OF RICHARD P. TAYLOR ( ues in the range of 1.3 to 1.5, regardless of Interestingly, the value increased over the Clearly, the computer’s expertise in the pattern’s origin. More recently, I decade that he made drip paintings, from detecting the fundamental characteristics teamed up with psychologist James A. 1.12 in 1945 up to 1.7 in 1952 and even of painted patterns offers art historians Wise of Washington State University, and up to 1.9 in a painting that Pollock de- and theoreticians a promising new tool. It windstorm painting we showed that this visual appreciation stroyed. It is curious that Pollock would will join infrared, ultraviolet and x-ray has an effect on the observer’s physiolog- have spent 10 years reﬁning his drip tech- analysis, which art experts already em- Pollock and Lee Krasner ical condition. Using skin conductance nique to yield high-D fractals if people ploy routinely, in a growing collection of tests to measure stress levels, we found that prefer low-range to midrange values. The scientiﬁc methods for investigating such midrange D values also put people at ease. increased intricacy of high D values, how- features of art as the images hidden un- Of course, these inquiries are just a begin- ever, may engage the attention of viewers derneath subsequent layers of paint. Per- ning; still, it is interesting to note that many more actively than the “relaxing” mid- haps it may even be able to throw a nar- of the fractal patterns surrounding us in range fractals and thus may have been in- row beam of light into those dim corners ); COURTESY OF RICHARD P. TAYLOR ( nature have D values in this same range— tuitively attractive to the artist. My cur- of the mind where great paintings exert

1947 clouds, for example, have a value of 1.3. rent work at the University of Oregon is their power.

RICHARD P. TAYLOR began puzzling over the paintings of MORE TO EXPLORE Jackson Pollock while head of the condensed-matter The Fractal Geometry of Nature. B. B. Mandelbrot. W. H. Freeman and Company, 1977. physics department at the University of New South Wales Chaos. James Gleick. Penguin Books, 1987. in Australia. He is now a professor of physics at the Uni- Comet: Jackson Pollock’s Life and Work. Kirk Varnedoe in Jackson Pollock, by Kirk versity of Oregon, where he continues his analysis of Varnedoe, with Pepe Karmel. Museum of Modern Art, 1998. Splashdown. R. P. Taylor in New Scientist, Vol. 159, No. 2144, page 30; July 25, 1998. THE AUTHOR Pollock’s work and investigates chaos and fractals in a Fractal Analysis of Pollock’s Drip Paintings. R. P. Taylor, A. P. Micolich and variety of physical systems. He also has a master’s de- D. Jonas in Nature, Vol. 399, page 422; June 3, 1999. gree in art theory, with a focus on Pollock, from the Uni- Architect Reaches for the Clouds. R. P. Taylor in Nature, Vol. 410, page 18; ©DIGITAL IMAGE ©MUSEUM OF MODERN ART/LICENSED BY SCALA/ART RESOURCE, NEW YORK, ©2002 POLLOCK-KRASNER FOUNDATION/ARTISTS RIGHTS SOCIETY (ARS), NEW YORK (Full Fathom Five, COLLECTION OF ALBRIGHT-KNOX ART GALLERY, BUFFALO, N.Y., ©HANS NAMUTH ( versity of New South Wales. March 1, 2001.