Nonlinearity and distance of ancient routes in the Aztec Empire.

This study explores the way in which traveling paths in ancient cultures are characterized by the relationship between nonlinear shapes and path lengths in terms of distances. In particular, we analyze the case of trade routes that connected Aztec settlements around 1521 CE in central Mexico. Based on the complex systems perspective, we used the least cost path approximation to reconstruct a hypothetical large-scale map of routes reproducing physical connections among ancient places. We compared these connections with different spatial configurations and identified the probability distribution functions of path lengths. We evaluated the nonlinearity using the mean absolute error based on the path fitness of simple linear models. We found asymmetrical distributions and positive relationships between those measures. If a path length increases, so does its nonlinearity. Thus, the simple pattern of traveling in the Aztec region is fairly unlikely to be straight and short. Complex pathways can represent most of the ancient routes in central Mexico.