Mathematics shows how the composition of landscape paintings has changed over time

Whether it’s a tree in the foreground or a ship in the distance, artists have put a lot of thought into the placement of each element on the canvas. Today, researchers from the Korea Advanced Institute of Science and Technology and National Chungbuk University in Korea used a new method to find out how the composition of paintings has changed over time in Western art. By digitally analyzing thousands of paintings, they found that the average horizon placement in landscape paintings has changed slightly over the years.

The researchers collected 14,912 images of landscape paintings from the WikiArt and Web Art Gallery databases and wrote a program to interpret some aspect of these digital images. The paintings dated from the Renaissance through modern times, and the question the team attempted to answer was whether they could see any patterns or trends in the way these landscapes were composed.

The composition of a painting roughly describes which element goes where, and which part of the canvas occupies each part of the painting. It is not unique to painting. Introductory photography courses often teach students the “rule of thirds” – a guideline that requires the photographer to mentally divide the image into thirds and place important elements on imaginary horizontal and vertical lines. If a future art historian were to analyze all of the photographs taken by every photographer who abides by this rule of thirds, and measure where the horizontal and vertical lines are in the final photos, he could see this pattern of thirds emerge.

That’s pretty much what the researchers did here. In a recent article in PNAS they describe how they designed an algorithm to identify areas in images that matched horizontal or vertical lines. They specifically looked at landscape images, as these very often have clearly pronounced horizontal and vertical lines on the horizon, buildings, trees, and cliffs.

The algorithm compared the colors of the individual pixels in each image to first find the most prominent horizontal or vertical line that divides the canvas in half. Then it moved to find the line that divides the next larger area in half, and so on.

Since the collection of images used in this study consisted entirely of landscape paintings, the most important dividing line in most of the images was the horizon. And when the researchers looked at the data for all of these images that were divided by a clear horizontal horizon, they noticed that the horizon has shifted slightly over the years. In 16th century paintings, the horizon was higher than in late 17th century paintings. Then the lower horizons were the norm until the middle of the 19th century, when they again moved upwards.

Along with specific weather trends such as the changing horizon, the team also checked their data to see if they could find any local trends. After all, some artistic styles are often regional. But when it comes to composition, the trends did not seem to follow any regional pattern. However, the researchers point out in their to study that they were primarily interested in Western art, so this is not necessarily true for all art.

This type of analysis is not limited to paintings. The same techniques could be used to study compositional patterns in films, typography, or photography, for example. This could be a way to quickly assess a large number of pieces to find a pattern or trend, as this study did. But we cannot leave the analysis of art entirely to computers. It is simply a possible starting point for a more in-depth analysis of art history, as an algorithm can only find patterns, not understand the human intentions behind them.