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Chaos by design

Chris Holt describes how revolutionary mathematics gives fresh insights into the work of Jackson Pollock

Jackson Pollock painted "Summertime: Number 9A" in 1948. It has an extraordinary format - 5.5 metres wide but only 85 cm high. Lyrical, dancing movements have been created by pouring black paint onto the canvas in a sweeping pattern of intertwined flowing lines. Some interstices have been filled in with colour. A brush has been used (unusual for Jackson Pollock at this stage) to add green dots and short yellow lines. The painting has the characteristic Jackson Pollock features: a uniformity over most of the canvas, and a painting without depth or focal point.

In a famous film of the artist, he prowls around a huge piece of canvas laid out on the floor of a barn. He attacks from all sides, using sticks and trowels to throw paint at the canvas. He pours paint from cans directly onto the canvas and spatters many layers until the paint is very thick.

Glass tubes with rubber bulbs on one end are used to squirt paint. When these become clogged he hurls them onto the canvas where they break, scattering glass shards which become embedded in the wet paint.

Jackson Pollock was one of the most innovative painters of the 20th century. His large bold canvases have been described as "all-over" paintings; filled with a more-or-less uniform distribution of painted detail, many lines loop and arc across them. There is no depth, the paintings exist only in the picture plane. In some later ones, lines fill the entire canvas leaving no unpainted spaces at all. When his paintings were described by an art critic as being the product of accident, he said:

"I do have a general notion of what I'm about and what the results will be.

I can control the flow of paint, there is no accident."

Despite becoming a famous painter, Jackson Pollock was a very troubled personality. Friends say he was a full-blown alcoholic by the age of 16.

One of his brothers described him as manic-depressive and self-destructive.

For a few years Jackson Pollock was very productive and became world-famous. But in the last years before his death, his alcohol consumption steadily increased and his creativity declined. On August 11, 1956, after an evening of heavy drinking, he set off for a concert in his old Ford. The car hit a tree and Jackson Pollock was killed. One passenger died and the other was badly injured. The journalist Sally Vincent wrote:

"It was an accident. One of those things that Pollock, in his work, insisted never happened."

Twenty years after Jackson Pollock's death, a major revolution was taking place in mathematics. Benoit Mandelbrot created fractal geometry, a fusion of maths and the natural world. Traditional geometry can only describe simple shapes such as circles, triangles and cubes. Fractal geometry was spectacularly successful in describing complex structures found in nature, such as trees, clouds or blood vessels in the human body. Fractal geometry describes the recurrence of patterns at progressively finer scales, whereby at any magnification they show a similar appearance. This was a key to understanding the natural world and fractal geometry went on to become a discipline in its own right.

Richard Taylor is a physicist who trained as a painter at the Manchester School of Art. In 1999 he analysed some of Jackson Pollock's paintings to determine whether the patterns were fractal. He placed square grids over scanned photos of the paintings and counted the number of squares which contained paint. This was repeated a number of times as the size of the squares was reduced. The log of the number of squares containing paint was plotted against the log of the size of the square - a straight line indicates fractal geometry because the pattern remains the same whatever the size of the square. The slope of the line (the inclination from the horizontal) is called the fractal dimension, the size of which reflects the complexity of the pattern. Straight lines were indeed the result.

The fractal dimension of Jackson Pollock's paintings increased steadily, from close to 1 (a slope of 45 LESS THAN ) in 1943 to 1.72 (a slope of 60 LESS THAN ) in 1952.

Taylor is confident he can determine the date of a Jackson Pollock painting by measuring its fractal dimension. We now see Jackson Pollock's paintings in a new light. They have the same quality as many images in the natural world. He was not mimicking nature, he was describing it directly.

In a subsequent study, Taylor showed people fractal and non-fractal patterns in which the same total area was coloured in. He found that people definitely preferred images with a fractal dimension in the range 1.3 to 1.5 over non-fractal patterns.

Did Jackson Pollock realise that his paintings described nature? Maybe. In 1956, shortly before his death, he said his paintings were "very representational some of the time, and a little all of the time". Readers might consider this inaccurate but, now that we have a better understanding of the maths underlying images of the natural world, we can say that Jackson Pollock's remark was, in fact, spot-on.

Dr Chris Holt is a freelance science writer

Paul Jackson Pollock

1912 - 1956

Born in Wyoming, Jackson Pollock became interested in art at the age of 10, when his brother Charles sent him the art magazine, The Dial. In 1943, the year of his first drip painting, he had his first one-man show in New York; by 1947 this was his main style. His paintings were a world-wide success, and in 1949 Life magazine asked: "Is he the greatest living painter in the United States?" Seven years later, he was dead in a car crash, drunk at the wheel.

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