Quantifying patterns in art and nature. Issue 2 (3rd April 2021)

• Record Type: Journal Article
• Authors: Balmages, Amanda; Schiffman, Lucille; Lyle, Adam; Lustig, Elijah; Narendra-Babu, Kavya; Elul, Tamira
• Is Part Of: Journal of mathematics and the arts. Volume 15:Issue 2(2021)
• Page Start: 188
• Page End: 197
• Publication Date: 2021-04-03
• Subjects: Natural fractal patterns -- order and disorder -- fractal dimension -- Burtynsky -- photography; Arts -- Mathematics -- Periodicals; 700.151
• DOI: 10.1080/17513472.2021.1922238
• Languages: English
• ISSNs: 1751-3472

Abstract

Abstract : 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: UF0001