Abstract
We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function (PDF) of luminance fluctuations of points (pixels) separated by a distance R compares notably well with the PDF of the velocity differences in a turbulent flow, as predicted by the statistical theory of A.N. Kolmogorov. We observe that turbulent paintings of van Gogh belong to his last period, during which episodes of prolonged psychotic agitation of this artist were frequent. Our approach suggests new tools that open the possibility of quantitative objective research for art representation.
Similar content being viewed by others
References
Livingstone, M.S.: Vision and Art: The Biology of Seeing. Harry N. Abrams, New York (2002)
Space Phenomenon Imitates Art in Universe’s Version of van Gogh Painting. HUBBLESITE newscenter, News Release Number STScl-2004-10. http://hubblesite.org/newscenter/archive/releases/2004/10/. Acces date: October 1, 2007
Kolmogorov, A.N.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303 (1941). Reprinted in Proc. R. Soc. Lond. A 434, 9–13 (1991)
Kolmogorov, A.N.: Dissipation of energy in the locally isotropic turbulence. Dokl. Akad. Nauk SSSR 32, 16–18 (1941). Reprinted in Proc. R. Soc. Lond. A 434, 15–17 (1991)
Kolmogorov, A.N.: A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds numbers. J. Fluid. Mech. 13, 82–85 (1962)
Ghashghaie, S., Breymann, W., Peinke, J., Talkner, P., Dodge, Y.: Turbulent cascades in foreign exchange markets. Nature 381, 767–770 (1996)
Kemp, M.: From science in art to the art of science. Nature 434, 308 (2005). See also the section “Artists on science: scientists on art” in the same number
Taylor, R.P., Micolich, A.P., Jonas, D.: Fractal analysis of Pollock’s drip paintings. Nature 399, 422 (1999)
Mureika, J.R., Dyer, C.C., Cupchik, G.C.: Multifractal structure in nonrepresentational art. Phys. Rev. E 72, 046101 (2005)
Hunt, R.W.G.: Measuring Colour. Fountain, Bibvewadi (1998)
González, R.C., Woods, R.E., Eddins, S.L.: Digital Image Processing Using MATLAB. Prentice Hall, New Jersey (2003)
Obukhov, A.M.: Some specific features of atmospheric turbulence. J. Fluid. Mech. 13, 77–81 (1962)
Castaing, B., Gagne, Y., Hopfinger, E.J.: Velocity probability density functions of high Reynolds number turbulence. Physica D 46, 177–200 (1990)
Mitra, D., Bec, J., Pandit, R., Frisch, U.: Is multiscaling an artifact in the stochastically forced Burgers equation? Phys. Rev. Lett. 94(194501) (2005)
Arnold, W.N.: The illness of Vincent van Gogh. J. Hist. Neurosci. 13, 22–43 (2004)
Harrison, R. (ed.): The Complete Letters of Vincent van Gogh. Bulfinch, Minnetonka (2000)
Peck, A.: Beginning the GIMP: From Novice to Professional. Apress, China (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Aragón, J.L., Naumis, G.G., Bai, M. et al. Turbulent Luminance in Impassioned van Gogh Paintings. J Math Imaging Vis 30, 275–283 (2008). https://doi.org/10.1007/s10851-007-0055-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10851-007-0055-0