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columbia outlet Multiscale analysis is also at the heart of Richard Taylor's approach to Pollock. Taylor's investigation shave not been driven by questions of provenance (although due to the frequent requests for authentication he has set-up a non-profit company to manage this work as well as to protect himself in the case oflaw suits). He is mainly interested in the work, as both a scientist and anartist. He had taken a year's leave at one point in his career to devote himself to his own painting, but after a year decided that he was better off not quitting his day job. He brings a physicist's eye to the arts, and in the case of Pollock, it has been a perfect storm of art and science that has enabled Taylor to find his own research in the works of this abstract expressionist master-the "chaos" for which one critic famously denounced Pollock's work in the 1950s is something that Taylor saw quite literally as the mathematics of fractal geometry. The word "fractal" was coined in 1967 by the IBM mathematician Benoit Mandelbrot to encompass the geometric character of natural objects. The perfect lines, planes, and spheres of Euclidean geometry are Platonic abstractions, good for a first approximation to things like coastlines, landscapes, and clouds, but clearly fall short at describing the variation ofthe natural world. Mandelbrot noticed that the character of such natural phenomena was a similarity in scale-that at each increase in magnification, the structures of nature, complicated though they are ("fractal" is derived from the same root as fragment and fracture), repeat themselves, maybe not precisely, but to a degree that can be quantified. The crags of a mountain range are replicated in the nooks and crannies of the stones that comprise them, or the eddies of a turbulent river flow are themselves composed of eddies within eddies, within eddies. 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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