Session W5: Physics Meets Art

Quasicrystals in Medieval Islamic Architecture

The conventional view holds that girih (geometric star-and-polygon) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, and drafted directly with a straightedge and a compass. I discuss our recent findings that, by 1200 A. D., a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (girih tiles) decorated with lines. These girih tiles enabled the creation of increasingly complex periodic girih patterns, and by the 15th century, the tessellation approach was combined with self-similar transformations to construct nearly-perfect quasicrystalline patterns. These patterns have remarkable properties; they do not repeat periodically, and have special symmetry---and were not understood in the West until the 1970s. I will discuss some of the properties of Islamic quasicrystalline tilings, and their relation to the Penrose tiling, perhaps the best known quasicrystal pattern.   

The Story of the Water Cube

The National Aquatics Center or ``Water Cube,'' constructed for the Beijing Olympics, is unusual in that its very structure has a physical significance. It consists of a massive framework of steel beams that are arranged as in the Weaire-Phelan structure of an ideal foam, with an outer facing of transparent ``cushions.'' Brilliantly conceived by Tristram Carfrae of the Arup Corporation, it makes a spectacular impression on those who enter. It provokes thoughts on aesthetics, order/disorder, optimisation, and the frequent recurrence of bubbles/foams in our literary and artistic culture. The story of the Water Cube will start in the nineteenth century, when William Thomson (Lord Kelvin) first posed the problem: what kind of foam of equal-sized bubbles minimises area (or energy)?   

The Drip Paintings of Jackson Pollock: Are They Really fractal?

It has been claimed the drip paintings of late Abstract Expressionist painter Jackson Pollock can be usefully characterized as fractal, and that fractal analysis can be used to authenticate works of unknown origin. This academic issue has become of more general interest following the recent discovery of a cache of disputed Pollock paintings. I will demonstrate that this hypothesis of ``Fractal Expressionsim'' is fundamentally flawed, and that fractal analysis as an authentication tool yields inconsistent and unreliable results. This work has also led to two new results in fractal analysis of more general scientific significance. First, the composite of two fractals is not generally scale invariant and exhibits complex multifractal scaling in the small distance asymptotic limit. Second the statistics of box-counting and related staircases provide a new way to characterize geometry and distinguish fractals from Euclidean objects.   

Learning from Monet: A Fundamentally New Approach to Image Analysis

The hands and minds of artists are intimately involved in the creative process, intrinsically making paintings complex images to analyze. In spite of this difficulty, several years ago the painter David Hockney and I identified optical evidence within a number of paintings that demonstrated artists as early as Jan van Eyck (c1425) used optical projections as aids for producing portions of their images. In the course of making those discoveries, Hockney and I developed new insights that are now being applied in a fundamentally new approach to image analysis. Very recent results from this new approach include identifying from Impressionist paintings by Monet, Pissarro, Renoir and others the precise locations the artists stood when making a number of their paintings. The specific deviations we find when accurately comparing these examples with photographs taken from the same locations provide us with key insights into what the artists' visual skills informed them were the ways to represent these two-dimensional images of three-dimensional scenes to viewers. As will be discussed, these results also have implications for improving the representation of certain scientific data. Acknowledgment: I am grateful to David Hockney for the many invaluable insights into imaging gained from him in our collaboration.