Amirshahi, Seyed Ali & Hayn-Leichsenring, Gregor & Denzler, Joachim & Redies, Christoph. (2014). Evaluating the Rule of Thirds in Photographs and Paintings. Art & Perception. 10.1163/22134913-00002024.
“The rule of thirds (ROT) is one of the best-known composition rules used in painting and photography. According to this rule, the focus point of an image should be placed along one of the third lines or on one of the four intersections of the third lines, to give aesthetically pleasing results.”
this webpage from Digital Photography School also provides in-depth explanation of the idea in Rule of Thirds.
Anger Photography 