Comparative Study in Art : The Zipf’s Law

The Zipf’s law is an empirical law, first observed when ranking words according to their occurrence in a text [1]. Zipf’s law is also known to hold in many other areas, for example when ranking cities according to its population number, when counting notes in music [3] or pixels in pictures. Recently, we started to use Zipf’s law as a tool for a comparative study in art, via the statistical analysis of digitalised paintings. We developed a code to count and rank all pixels of a given digital photography for a given painting. We compared the frequency distribution of different movements such as Cubisme, Impressionisme, Expressionism , Neoclassicism, Pre-Raphaelite and Surealisme. For each movement we selected seven of the most famous artists such as Fernand Leger, Pablo Picasso, Georges Braques as cubists and Pierre A. Renoir, Eugene Boudin, Claude Monet as impressionists. Finally for each artist, we selected seven paintings which are systematically submitted to the same numerical analysis. When possible we evaluated the “average” for every artist. There are other statistical tools one can use to study paintings. One can think of  a digitalised painting as a 2D square lattice, with on each site, a vector with 3 components (x,y,z) representing a pixel with the colour information (R,G,B). It is therefore possible to define correlation function between sites. This work is currently in progress and I hope to be able to publish an update pretty soon.

[1] Zipf G. K., The Psychobiology of Language. Houghton-Mifflin, 1935

[2] Zipf G. K., Human Behaviour and the Principles of Least Effort, Addison-Wesley, 1949.

[3] Bill Manaris, Juan Romero, Penousal MacHado, Dwight Krehbiel, Timothy Hirzel, Walter Pharr and Robert B. Davis Zipf’s Law, Music Classification, and Aesthetics Computer Music Journal, Vol. 29, No. 1 (Spring, 2005), pp. 55-69, The MIT Press

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