Quantifying patterns in art and nature

Many different types of artworks mimic the properties of natural fractal patterns – in particular, statistical self-similarity at different scales. Here, we describe examples of abstract art created by us and well-known artists such as Ruth Asawa and Sam Francis that evoke the repetition and variability of biological forms. We review the ‘drip’ paintings of Jackson Pollock that display statistical self-similarity at varying scales, and discuss studies that measured the fractal dimension of Pollock’s drip paintings. The contemporary environmental artist Edward Burtynsky who captures aerial photographs of man-created and man-altered landscapes that resemble natural patterns is also discussed. We measure fractal dimension and a second shape parameter – fractional concavity – for borders in three of Burtynsky’s photographs of man-made landscapes and of biological tissues that resemble his compositions. This specifies the complexity of patterns in Burtynsky’s photographs of diverse man-impacted landscapes and underscores their similarity to fractal patterns found in nature. Graphical Abstract: Log Booms # 1. Photograph © Edward Burtynsky, courtesy Robert Koch Gallery, San Francisco / Nicholas Metivier Gallery, Toronto. GRAPHICAL ABSTRACT