skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Order-fractal transitions in abstract paintings

Abstract

In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition frommore » Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.« less

Authors:
 [1];  [2];  [3]
  1. Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, RS (Brazil)
  2. Department of Applied Physics, CINVESTAV-IPN, Carr. Antigua a Progreso km.6, Cordemex, C.P.97310, Mérida, Yucatán (Mexico)
  3. Department of Informatics, Universidad Politécnica de Puebla, 72640 (Mexico)
Publication Date:
OSTI Identifier:
22560338
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 371; Journal Issue: Complete; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CULTURAL OBJECTS; DATA ANALYSIS; DIMENSIONS; FRACTALS; HISTORICAL ASPECTS; METRICS; ORDER-DISORDER TRANSFORMATIONS

Citation Formats

Calleja, E.M. de la, E-mail: elsama79@gmail.com, Cervantes, F., and Calleja, J. de la. Order-fractal transitions in abstract paintings. United States: N. p., 2016. Web. doi:10.1016/J.AOP.2016.04.007.
Calleja, E.M. de la, E-mail: elsama79@gmail.com, Cervantes, F., & Calleja, J. de la. Order-fractal transitions in abstract paintings. United States. doi:10.1016/J.AOP.2016.04.007.
Calleja, E.M. de la, E-mail: elsama79@gmail.com, Cervantes, F., and Calleja, J. de la. Mon . "Order-fractal transitions in abstract paintings". United States. doi:10.1016/J.AOP.2016.04.007.
@article{osti_22560338,
title = {Order-fractal transitions in abstract paintings},
author = {Calleja, E.M. de la, E-mail: elsama79@gmail.com and Cervantes, F. and Calleja, J. de la},
abstractNote = {In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.},
doi = {10.1016/J.AOP.2016.04.007},
journal = {Annals of Physics},
number = Complete,
volume = 371,
place = {United States},
year = {Mon Aug 15 00:00:00 EDT 2016},
month = {Mon Aug 15 00:00:00 EDT 2016}
}