Scaling the living space: Zipf’s law for traditional courtyard houses in South China

In the traditional feudalistic society of China, there is a characteristic residential pattern of several core families with common ancestors living together in one house, as far as possible. Hence, the habitation of large families and their social dynamic always have a complex function and hierarchical structure. In this article, we consider a courtyard in South China as an example to enable a discussion of the mathematical relationship among the five basic functional spaces in it. Based on Zipf’s law, we find that the distribution of the five types of spaces, from large to small, can be described by the Pareto distribution with a shape parameter close to −1. Moreover, the Zipf parameters of different houses in the same area conform to the double Pareto distribution. This suggests that the size and shape of a residence also follows well-defined scaling laws. Additionally, it indicates that houses, at least traditional Chinese houses, have strong self-organization and self-similarity. It also shows that the power law of the Pareto distribution is applicable not only to the macro scale of the city but also the micro scale of housing.