Artistic painting: A fractional calculus perspective

Abstract

• Application of information theory in the analysis of painting evolution during the last 7 centuries. • Fractional order description of paintings. • Analysis of painting by means of fractional entropy. This paper studies artistic paintings by means of information theory and fractional calculus. A set of artworks created by 100 artists in a time scale covering the last seven centuries of the human kind, is characterized through different entropy indices. First, the paintings are converted into digital format and discretized. Afterwards, the data for color and grayscale images are processed by means of the Shannon and the fractional entropies, both for 1- and 2-dim histograms. The results are correlated with artistic movements that took place throughout the history of painting. In a second phase, the similarities between artists are analyzed for various periods of time. A sample of 10 artworks per artist is considered and their 2-dim fractional entropy is calculated for time scales of 700 and 130 years. The data are processed by a hierarchical clustering algorithm and the results interpreted under the light of the emerging clusters. Finally, the works of a single artist are compared during a short time scale of 47 years.