Journal of Mathematical Imaging and Vision

, Volume 30, Issue 3, pp 275–283 | Cite as

Turbulent Luminance in Impassioned van Gogh Paintings

  • J. L. AragónEmail author
  • Gerardo G. Naumis
  • M. Bai
  • M. Torres
  • P. K. Maini


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.


Probability Distribution Function Foreign Exchange Market Semilog Plot Famous Painting Spanish National Research Council 
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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • J. L. Aragón
    • 1
    Email author
  • Gerardo G. Naumis
    • 2
  • M. Bai
    • 3
  • M. Torres
    • 4
  • P. K. Maini
    • 5
  1. 1.Centro de Física Aplicada y Tecnología AvanzadaUniversidad Nacional Autónoma de MéxicoQuerétaroMexico
  2. 2.Instituto de FísicaUniversidad Nacional Autónoma de MéxicoMéxicoMexico
  3. 3.School of Electronic Information EngineeringBeijing University of Aeronautics and AstronauticsBeijingChina
  4. 4.Instituto de Física AplicadaConsejo Superior de Investigaciones CientíficasMadridSpain
  5. 5.Centre for Mathematical BiologyMathematical InstituteOxfordUK

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