The Abstract Expressionists and Les Automatistes: A shared multi-fractal depth?

Statistical analysis of abstract paintings is becoming an increasingly important tool for understanding the creative process of visual artists. We present a multifractal analysis of 'poured' paintings from the Abstract Expressionism and Les Automatistes movements. The box-counting dimension (D 0) is measured for the analyzed paintings, as is the associated multifractal depth DD¼D 0 À D N , where D N is the asymptotic dimension. We investigate the role of depth by plotting a 'phase space' diagram that examines the relationship between D 0 and D N. We show that, although the D 0 and D N values vary between individual paintings, the collection of paintings exhibit a similar depth, suggesting a shared visual characteristic for this genre. We discuss the visual implications of this result. In 1945, Jackson Pollock started to perfect a radically new approach to painting. Abandoning physical contact with the canvas, he dipped his brush in and out of a can and poured the fluid paint onto horizontal canvases. The uniquely continuous paint trajectories served as artistic 'fingerprints' of his motions through the air. Over the next decade, he generated vast abstract works featuring complex patterns formed across many scales—from the width of the canvas down to finest speck of paint. In doing so, he became one of the leaders of the Abstract Expressionist movement, which shifted the focus of the art world from its traditional base of Paris to New York. Pollock's form of Abstract Expressionism inspired the Quebec-based Les Automatistes who also adopted the pouring style of painting. Art theorists now recognize the ''drip and pour'' style as a revolutionary approach to esthetics. However, despite the millions of words written about this body of work through the years, the artistic significance behind these complex swirls of paint remained the source of fierce debate in the art world. One of the central questions within this debate concerned the degree of variability between paintings by different artists: for example, are there shared visual characteristics between Pollock's paintings and those of Les Auto-matistes? Examples of their respective works are shown in Figs. 1 and 2. Fractal analysis techniques hold great promise for both the academic and artistic communities, since these techniques serve to identify underlying visual signatures in an artwork. The fractal dimension D F of an artwork can be regarded as a preliminary indicator of complexity in a pattern: lower fractal dimensions are a measure of …