  Art is the ultimate expression of human creativity that is deeply influenced
by the philosophy and culture of the corresponding historical epoch. The
quantitative analysis of art is therefore essential for better understanding
human cultural evolution. Here we present a large-scale quantitative analysis
of almost 140 thousand paintings, spanning nearly a millennium of art history.
Based on the local spatial patterns in the images of these paintings, we
estimate the permutation entropy and the statistical complexity of each
painting. These measures map the degree of visual order of artworks into a
scale of order-disorder and simplicity-complexity that locally reflects
qualitative categories proposed by art historians. The dynamical behavior of
these measures reveals a clear temporal evolution of art, marked by transitions
that agree with the main historical periods of art. Our research shows that
different artistic styles have a distinct average degree of entropy and
complexity, thus allowing a hierarchical organization and clustering of styles
according to these metrics. We have further verified that the identified groups
correspond well with the textual content used to qualitatively describe the
styles, and that the employed complexity-entropy measures can be used for an
effective classification of artworks.
