Science and Culture: Charting the history of Western art with math.

For more than a century, researchers have used statistics to study writing style in a sort of literary forensics technique called stylometry. In 1901, physicist T. C. Mendenhall famously measured word-length frequency in William Shakespeare’s works and reported that the writer’s style was awfully close to that of fellow writer Christopher Marlowe, fueling rumors that the lattermayhavewrittenworks attributed to the former. The techniques are still in use: In 2013, stylometric software unmasked “Robert Galbraith,” author of the acclaimed crime fiction novel The Cuckoo’s Calling, as J. K. Rowling, who penned the Harry Potter books. Stylometry reaches other arts, too. Computer scientists have unleashed algorithms on paintings, charting mathematical patterns in the artwork of masters like Jackson Pollack, Vincent van Gogh, Pieter Bruegel the Elder, and others (1–3). More recently a trio of Korean physicists undertook a massive project to quantify changes in the use of color and contrast in the history of Western art. Daniel Kim and Hawoong Jeong at the Korea Advanced Institute of Science and Technology in Daejeon, and Seung-Woo Son at Hanyang University in Ansan, analyzed the digital versions of 8,798 paintings from the Web Gallery of Art, an online database of European art created and maintained by a physicist and computer scientist in Budapest. Focusing on color use, color variety, and contrast, the physicists reported that over the last millennium or so, Western art has become brighter and has used more colors (4). To study contrast, the physicists used color data from a painting’s digital file to quantify the brightness of each pixel. The researchers translated that quantity into a height, creating a column on each pixel at the same position so that brighter spots stood taller than darker spots along the z axis. This technique effectively turned flat images into a sort of deep-pile carpet. (An example of the technique is shown in the images of St. John the Evangelist Drinking from the Poisoned Cup.) The physicists tracked changes in height across individual paintings, then averaged those changes across the paintings from a given period. By this measure, called the “roughness of brightness,” the use of contrast has increased over time. Their findings correspond with trends art historians have already reported. For example, the physicists noted that the contrast increased in paintings beginning with the Renaissance period, when painters started routinely using stark contrasts between dark and light, called chiaroscuro. To measure color use, the physicists used “chromo-spectrometry,” treating colors in paintings like words in a book by counting the occurrence of different colors. They used an algorithm to distinguish tens of thousands of different shades in different proportions. “If you are looking with bare eyes, it’s hard to tell how many colors are used,” says Kim. So, to quantify the variety of colors used, the physicists borrowed approaches from statistical physics often used to measure the dimensions of self-similar patterns, known as fractals. The fractal dimension of a geometric figure can be translated as a measure of its complexity. A straight line has a fractal dimension of 1. The fractal dimension of Great Britain’s wiggly coastline, by contrast, is 1.25. As applied to the new study, lower fractal dimension described a painting with a narrower palette. Again, the physicists saw results in line with art historians’ observations. For example, paintings created during the medieval period (roughly the 5th St. John the Evangelist Drinking from the Poisoned Cup portrays episodes from the life of the saint. Painted by medieval Italian painter Taddeo Gaddi, it dates between 1348 and 1353.