Debate ends on using fractal analysis for authenticating art

Where art and reality meet. Art experts and scientists will gather on Wednesday to talk about Jackson Pollock’s work, and Case Western Reserve University physicist Lawrence Krauss, the Ambrose Swasey Professor of Physics and Astronomy, will be among the invited guests to the symposium, sponsored by the International Foundation for Art Research in New York City. The program will take place at the National Academy of Design, and the gathering will examine science issues related to authenticating Jackson Pollock’s work. As it is, the university’s physicists recently “put the nail in the coffin” in the debate about using fractal analysis in authenticating art as they completed a second study related to fractal analysis and Jackson Pollock’s drip paintings. The debate over the veracity of fractal authentication ignited after fractal analysis was applied to a cache of paintings discovered by Alex Matter that may be works of Pollock. “No information about artistic authenticity can be gleaned from fractal analysis,” said Katherine Jones-Smith, lead author of the study. The researchers, which include physicists Jones-Smith and her collaborators Harsh Mathur and Lawrence Krauss, subjected seven paintings to fractal authentication and found that the fractal characteristics of a painting are completely uncorrelated to the artist. Their analysis includes three famous paintings by Pollock, two paintings from the Matter cache, and two paintings made earlier this year by Case Western Reserve undergraduates Alexandra Ash and Michael Hallen. In the process of analyzing art, the researchers discovered some new fractal mathematics and developed a process for separating the colored layers of paint in art works.

Fractal analysis involves placing a grid over an image to search for replications of geometric patterns. In this case, it also involved color separation and an analysis of each layer of paint. The data is plotted on a graph and a “box-counting curve” that resembles a staircase is generated. This curve is inspected to see if it meets the fractal authentication criteria. The fractal authentication criteria were developed by University of Oregon physicist Richard Taylor in a series of publications beginning with a 1999 Nature article. Taylor announced in 2006 that none of the six paintings that he analyzed from the Matter cache were authentic, according to his criteria. Later that year in an article published in Nature, Jones-Smith and Mathur reported that scribbles made by Jones-Smith using Adobe Photoshop also satisfied fractal authentication criteria, making them equal to Pollocks in mathematical complexity. That a drawing resembling a child’s picture of stars passed Taylor’s fractal test and rose to the status of a Pollock cast serious doubt on the validity of fractal analysis as an authentication tool.

You may want to read more about the end of the debate about fractal analysis and art authentication in yesterday’s Science Daily. “I think it is more appealing that Pollock’s work cannot be reduced to a set of numbers with a certain mean and certain standard deviation,” said Jones-Smith. “The mystique that is part of the human experience is not so simply classified and makes the tragedy of our existence more interesting,” said Krauss. Note that what started as artistic research did yield new mathematical findings about fractals. Mathur said they discovered that the statistics of box-counting curves and related staircases provide a new way to characterize geometry and distinguish fractals from Euclidean objects. They explored how the steps in the staircases deviated from a smooth box-counting curve to determine whether an object is fractal or Euclidean. “Aside from resolving this art matter, these considerations have lead to interesting scientific considerations,” said Krauss. “It is nice that consideration of the world of art has caused one to think about problems that are relevant in a more general way in physical system.”