Order-fractal transitions in abstract paintings

Abstract

We report the degree of order of twenty-two Jackson Pollock's paintings using Hausdorff-Besicovitch fractal dimension. Through the maximum value of each multi-fractal spectrum, the artworks are classify by the year in which they were painted. It has been reported that Pollock's paintings are fractal and it increased on his latest works. However our results show that fractal dimension of the paintings are on a range of fractal dimension with values close to two.We identify this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition through its dark paint strokes in Pollocks' paintings, as structured lines following a power law measured by fractal dimension. We obtain selfsimilarity in some specific Pollock's paintings, that reveal an important dependence on the scale of observation. We also characterize by its fractal spectrum, the called Teri's Find. We obtained similar spectrums between Teri's Find and Number 5 from Pollock, suggesting that fractal dimension cannot be completely rejected as a quantitative parameter to authenticate this kind of artworks.

History of art paintings through the lens of entropy and complexity

“…Among the seminal works, we have the article by Taylor et al (20), where Pollock's paintings are characterized by an increasing fractal dimension over the course of his artistic career. This research article can be considered a landmark for the quantitative study of visual arts, inspiring many further applications of fractal analysis and related methods to determine the authenticity of paintings (21)(22)(23)(24)(25) and to study the evolution of specific artists (26,27), the statistical properties of particular paintings (28) and artists (29)(30)(31), art movements (32), and many other visual expressions (33)(34)(35). The most recent advances of this emerging and rapidly growing field of research are comprehensively documented in several conference proceedings and special issues of scientific journals (36)(37)(38), where contributions have been focusing also on artwork restoration tools, authentication problems, and stylometry assessment procedures.…”

Beauty in artistic expressions through the eyes of networks and physics

“…But first applications happened only at the turn of the twenty-first century, where the work of Taylor et al [61] showed that Pollock's paintings are characterized by an increasing fractal dimension over the course of his artistic career. This subsequently inspired the application of fractal analysis to the authenticity of paintings [62][63][64][65][66], to the evolution of artists [67,68], to the statistical properties of paintings [69] and artists [70][71][72], to art movements [73] and to other visual expressions [74][75][76]. And we would be remiss not to mention that fractal art is a fascinating subject on its own right [77].…”

Complexity Analysis of Escher’s Art

“…Several complexity indices have been adopted to analyze art, namely entropy [ 18 , 19 ], Kolmogorov complexity [ 20 , 21 ], fractal dimension [ 22 , 23 ], and others [ 24 , 25 ]. Such indices are not independent, but they capture different aspects of the system state, complementing each other and leading to a deeper assessment of the subject under study [ 26 ].…”