Fractal analysis of a grocery store shopping path

The concept of a fractal has been applied to analyze the complex structure of various phenomena, including scale hierarchy in the natural sciences. In this study, we focus on the scale of customer shopping paths in a store and introduce fractal dimension as a quantified index to assess the complexity and nonlinearity of customer shopping paths. By applying box-counting analysis to the extracted shopping paths, we quantify the complexity of individual consumer behavior and delineate a relationship between customer movement and corresponding sales. We show that the average fractal dimension of the customer shopping path, which is related to the average stay-time in a store, is approximately 1.3. This is close to the fractal dimension of some natural phenomena (e.g., turbulence), including complex scale structures.