Thursday, January 22, 2009

The Facts on Pollock's Fractals

What do you do when you inadvertently discover a huge cache of paintings that may have been created by the American master Jackson Pollock? Have all of them verified by experts? Naturally. Set up a world tour then donate them to museums? Of course! Maybe even fire up the calculator for some non-Euclidian geometry?

Not so fast on that last one.

About ten years ago physicist Richard Taylor created quite a stir in the mathematics and art world when he claimed Pollock’s works contained unique mathematical patterns in his brush strokes. Taylor said that these mathematical patterns were fractal, and so unique one could actually identify whether any given work of art was a genuine Pollack based on these patterns. Fractals are extraordinary complex geometric patterns where shapes and configurations infinitely repeat themselves.

However a new soon to be published paper dispels this idea of using fractals to identify and date a Pollack work. Physicists Lawrence Krauss, Katherine Jones-Smith and Harsh Mathur of Case Western Reserve tested several of Pollock's most famous paintings against ones commissioned by local artists to see if the fractal identification would hold up.

It didn't. Not even close. Several of Pollock's most famous paintings failed the test, while other paintings created in 2007 by local artists showed up as the real thing. This work builds on a previous study in 2006 where Jones-Smith and Mathur showed the fractal patterns Taylor found were far too small to usefully identify a painting. The two were able to recreate these "Pollock fractals" by drawing crude freehand stars.

These new study shows pretty conclusively that Taylor's method for identifying works by Jackson Pollock using fractals is complete bunk. At the same time it also serves as a good word of caution about seeing things that may not be there. Fractal geometry in nature is a very trendy research subject right now. The idea that life can be broken down to numeric equations is exciting both in the sciences and pop culture. It was even the inspiration for Darren Aronofsky's mathematics-thriller Pi. At the same time, it's easy to go overboard. Mathematics explains so much about the physical world around us, but there are limits as to what it can predict. Fractals are a cutting edge field of research with applications across many of the sciences, but one has to be careful that each application is backed by hard evidence.

Or to quote the wizened old mathematics professor in the movie Pi, "[W]hen you abandon scientific rigor, you're no longer a mathematician, you're a numerologist!"

1 comment:

  1. Pollock authentication based on visual features is a special application of the extensive field of visual texture classification. Decades of research in this field--by computer vision experts, statisticians, and electrical engineers (rather than physicists)--shows that all successful methods use MULTIPLE FEATURES (as many as 47), not a single feature, be it fractal or otherwise. Moreover, even an apparently "useless" feature (i.e., one that provides no classification accuracy) can be essential to the success of classifiers based on multiple features. Recent experimental evidence shows that even though fractal features, taken alone, may not be useful, they may be useful as a supplement to other features, and even to other non-visual evidence. See the popular article here ( and the conference paper here ( Further information is available here (