Turbulent Luminance in Impassioned van Gogh Paintings

Authors:
J. L. Aragón;Gerardo G. Naumis;M. Bai;M. Torres;P. K. Maini
Affiliations:
Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Querétaro, Mexico 76000;Instituto de Física, Universidad Nacional Autónoma de México, México, Mexico 01000;School of Electronic Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing, China 100083;Instituto de Física Aplicada, Consejo Superior de Investigaciones Científicas, Madrid, Spain 28006;Centre for Mathematical Biology, Mathematical Institute, Oxford, UK OX1 3LB
Venue:
Journal of Mathematical Imaging and Vision
Year:
2008

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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.