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Mathematicians reduced the history of painting to a change in two parameters

Mathematicians have studied how, over the past thousand years, the pictures have changed the details and ordering of images. With the help of this method, scientists managed to formalize the main transitions that occurred in the history of painting, as well as classify the main directions. In the future, this approach will help to quantitatively study the history of the fine arts, as well as predict the main trends of its further development, the scientists writein the  Proceedings of the National Academy of Sciences .

Often, mathematical models that were originally created to describe physical processes find their application in completely different areas: for example, sports, art or sociology. Thus, using models from thermodynamics or solid state physics, scientists have succeeded in explaining the desire of people to assemble into complex groups and  describe the structure of the colonies that penguins create during the hatching of eggs.

In addition, for a formal description of certain phenomena in art or sports, new mathematical models are often developed, with the help of which it is possible to quantitatively study some seemingly exclusively qualitative processes. For example, in 1933, the American mathematician Birkhoff proposed using two parameters for describing the pictures that describe the structure of the images-complexity and entropy. The first of these quantities actually characterizes the number of details in the picture, and the second – the orderliness of their location.

However, in practice this approach began to be used relatively recently, when technical capabilities began to be allowed. Now, such methods, based on the study of fractal structure in paintings, are used, for example, to determine the authorship of paintings or to study the evolution of the manner of individual artists during life. This time scientists from Brazil, Slovenia and Austria, led by Haroldo V. Ribeiro from the Maringa State University, suggested using the same approach to study the history of painting.

To do this, the scientists used the WikiArt database , which collected about 140,000 works of different styles and written over a thousand years by more than 2,000 different artists. The images of all these pictures were reduced to a matrix representation in a gray scale, from which then for each of them two parameters were calculated: complexity and entropy. After that, the scientists looked at how the values ​​of these parameters change over time and depending on the style.

It turned out that the proposed approach makes it possible to clearly distinguish two transitions in the history of painting: from the classical period to the new art, and then from the new art to the newest. The first group includes representatives of medieval painting, the Renaissance, neoclassicism and romanticism. The second group of trends is impressionism and avant-garde genres of the first half of the 20th century (such as cubism, expressionism and surrealism). The third group is the art of postmodernity, which begins with the development of pop art in the 1960s.

Scientists have shown that it is possible to characterize fairly obvious transitions between these groups not only in qualitative terms of art history, but also within the framework of a formal model that is described by only two parameters. All the classical styles are in the range of intermediate values ​​of complexity and entropy. The transition to a new art led to an increase in the chaotic image and reduced detail, and the transition to the art of the second half of the XX century – on the contrary, a sharp increase in the complexity and orderliness of the image.

In addition, using the proposed approach, scientists were able to distinguish and characteristics of individual styles. It turned out that 92 different directions of painting, for which there were at least one hundred images in the database, it is possible to cluster and distinguish among them 14 main groups. The authors of the work note that they also managed to use these data to accurately determine the style of a particular picture using the methods of machine learning.

The scientists note that the classification they offer is a good description of the trends in the development of painting and can be used in the future as an effective method for classifying works of art. Nevertheless, the proposed method is based only on the analysis of the local structure of the images, therefore some aspects related to the composition of the pictures remain unaccounted for in this approach. According to the authors of the work, in the future with the help of such an approach one can not only study the pictures already written, but also predict the appearance of new styles – at least from the point of view of the local image structure.

The study of images through the analysis of their structure is used not only in the study of works of art. For example, recently scientists applied fractal analysis to Rorschach spots. As a result, researchers were able to find a direct relationship between the fractal dimension of the image and the number of associations it causes.

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