  Everything in the last period of Vincent van Gogh paintings seems to be
moving; this dynamical style served to transmit his own feelings about a figure
or a landscape. Since the early impressionism, artists emprically discovered
that an adequate use of luminance could generate the sensation of motion. This
sentation was more complex in the case of van Gogh paintings of the last
period: turbulence is the main adjective used to describe these paintings. It
has been specifically mentioned, for instance, that the famous painting
\emph{Starry Night}, vividly transmits the sense of turbulence and was compared
with a picture of a distant star from the NASA/ESA Hubble Space Telescope,
where eddies probably caused by dust and gas turbulence are clearly seen [1].
It is the purpose of this paper to show that the probability distribution
function (PDF) of luminance fluctuations in some impassioned van Gogh
paintings, painted at times close to periods of prolonged psychotic agitation
of this artist, compares notable well with the PDF of the velocity differences
in a turbulent flow as predicted by the statistical theory of Kolmogorov. This
is not the first time that this analogy with hydrodinamic turbulence is
reported in a field far different from fluid mechanics; it has been also
observed in fluctuations of the foreign exchange markets time series [2].

Fluid Dynamics