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This is a piece ofthe connection between chaos and fractal geometry-the chaos that we now know colloquially in the metaphor ofthe hurricane in Texas generated by the flapping wings of the butterfly over China is a phenomenon that when put into mathematical pictures (not unlike those that can be seen on The Weather Channel) give images that exhibit this sort of self-similarity. A famous example of a natural fractal is the irregular outline of the coast of England, which is, to a degree, replicated in any stretch of shore beneath the cliffs of Dover. British mathematician and polymath, Lewis Fry Richardson, was Mandelbrot's inspiration for the quantification of this irregularity in terms of its "fractal dimension," a number that effectively measures the complexity of a shape in terms of the degree to which it fills space at a given scale. The crinklier a line is, the more space it occupies in a box that surrounds it. Now, imagine a shape where as you crank up the magnification, that sort of "misbehavior" is replicated: You've got yourself a true fractal. A perfectly straight line has fractal dimension equal to one, while a square region has fractal dimension equal to two. Nature is generally somewhere in between: the coastline of England, the waves within waves of a stormy sea, the branches within branches of a fern leaf, our own circulatory or pulmonary system, or as it turns out, the skeins of paint in a Pollock drip painting. That is Taylor's discovery. When Pollock so famously said, "I am nature," or that "My concern is with the rhythm of nature ... the way the ocean moves," he was possibly closer to the truth than anyone gave him credit for and probably closer than he knew himself. Taylor has examined many of Pollock's works and found a remarkable degree of regularity in the fractal dimension that can be computed by examining different color layers in the paintings. Firstly, what is remarkable is that Pollock could regularly achieve fractal structure. Taylor's personal attempts at such a result were only successful when he came up with the idea of hanging a bed sheet from a tree and allowing the measurable fractal nature of the wind to be realized in dripped paint blown onto the sheet. Even more, there appears to be a fractal dimension to Pollock's work that is characteristic of a given period, so that Pollock did, over periods of time, reliably reproduce in his work a small range of fractal dimensions. In fact, Taylor claims even more, that in his examinations he finds evidence for two distinct fractal dimensions as might be predicted by a documented two-step working style in which Pollock would lay down a broad under layer to which he would later add detail. When presented with a would-be Pollock, Taylor performs the digital analysis and checks to see if the numbers jibe with those that have been computed for Pollock's known work of a given period. Taylor's analysis of the Matter collection suggested that the drip paintings were forgeries. However, in some related work, John Elton and Yang Wang of Georgia Tech; Jim Coddington, Chief Conservator at New York's Museum of Modem Art; and I have determined that a generalization of fractal dimension, called multifractal analysis, may provide a more textured signature for the work. It's significant that Taylor found a digital signature for Pollock. But what might be even more significant is that the art world paid attention to it, for this shows the art/science boundaries are continuing to become fuzzier and fuzzier. Presumably, this is just the beginning, although there will surely be artists whose work defeats a statistical approach. In the spring of2007, five teams of researchers will converge on the Van Gogh Museum in Amsterdam to present the results of a year-long study aimed at uncovering a digital signature for Vincent van Gogh. And other methods of this type of work are emerging. An interesting and very general approach to finding a style in any digital media is work of the Dutch information theorist Paul Vitanyi, whose analysis focuses on the information content (in a statistical sense) of the work. His media-free approach is one that allows any collection of numbers to be compared to any other, making possible the idea of comparing works of art to works of literature. Stylometry opens us up to a world in which we are defined by our digital trail-the words we write, the websites we visit, the pictures we store, summarized in a statistical fingerprint. We are our actions. How very existential.

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In May 2005, Alex Matter, a filmmaker and son of the photographer Herman Matter and painter Mercedes Matter, announced the discovery of32 early Jackson Pollock drip paintings. The full story sounded a lot like a New York version of Michael Frayn's novel Headlong. Matter's parents were friends of Pollock, close enough to the artist that photographs exist of them lounging about with Pollock. At least one biography of Pollock mentions the purchase of some small Pollock works by the Matters, and it is reported that Herman Matter's signature is on the back of these works, labeling them as Pollock originals. It seems that the paintings had been languishing in a metal storage bin out on Long Island until they were discovered by Mr. Matter, not far from Pollock's former home in the Hamptons and the scene of his fatal car accident. The press releases were accompanied by pictures of a grinning Alex Matter holding one of these paintings, which, at a distance and at the resolution of a newspaper photograph, looked suitably spattered. It's a good story and certainly a plausible one. But, in fact, hardly a year goes by in which someone doesn't claim to have found a long-lost Pollock- that's what Richard Taylor, a consultant for the Pollock-Krasner Foundation tells me. Most of these claims are disposed of easily, their faults ranging from the obvious (misspelled signatures-"Jackson Pollack") to the subtle (materials that were only available after Pollock's death). Some fakes are veterans of the auction circuit and reappear every few years with a new story ("Some hitchhiker gave this to a truck driver, who brought it into my gallery ... "), while other schemes are almost as ingenious as the artist himself, even going to the extremes of inventing a provenance by inserting appropriately faded pictures of the "discovered" work into obscure hard-to-find gallery catalogs. So, how to tell real from fake In spite of the fact that there is only one right answer, generally, evaluating claims of authenticity in the world of modem art is, well, more art than science. Slamdunks are the situations in which the work is accompanied by an airtight provenance, consisting of documentation of every single person or institution that has ever owned the work (the back of a painting can look like a well traveled steamer trunk, covered with labels marking its appearance in exhibitions). Such works are also accompanied by records of any conservation incurred and a list of events detailing the touch-up here or the cleaning there. Failing this sort of complete biography, the truth begins to get a little murkier. Sometimes science can help. X-rays can reveal under paintings or preliminary sketches. Analysis of the materials provides clues, including information as to the age of the work. But even this hard evidence can go only so far. Several years ago the photography market was flooded with "newly discovered" Man Ray prints, their authenticity supported by the fact that the photographic paper was exactly of the kind that Man Ray was known to have used 60 years ago. It was only later discovered that the forger had managed to find an old cache of this paper, obtain access to Man Ray's negatives, and use this to make a new set of prints. So, enter the human actor. Connoisseurs steeped in the work of the artist in question apply the "sniff test" and either the light bulb goes on or it doesn't. And the fact is that different connoisseurs of the same artist can have different senses of smell. Ultimately, in the case of Alex Matter's bundle of proposed Pollocks, the experts are taking a close look at each painting and answering the question, "Is this work characteristic of the style of Jackson Pollock at this stage in his career" This is the question that Richard Taylor asked when the PollockKrasner Foundation called him in to evaluate the Matter cache-but the way in which he differs from his connoisseur colleagues is that he answered the question with mathematics. Taylor seems to have found a way to extract a numerical signature that identifies a work as an original Pollock. More precisely, Taylor has determined that a statistical analysis of the numbers that comprise the digital representation of the work can reliably separate authentic Pollocks from fakes. In so doing, Taylor's work is paving the way for a new world of visual "stylometry," that is, a growing discipline that is making math out of that seemingly impossible to define thing that is style. It is a subject that actually goes back to the mid-1800s, but has recently exploded in our world in which all actions and creations are fodder for broad vision. The tools of trade find their way into all aspects of our life, helping to distill not only styles of artistic creation, but styles of all sorts of actions.

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