Settlement percolation: A study of building connectivity and poles of inaccessibility

Abstract

In many countries and regions there is a strong interest in limiting urban sprawl and further land consumption. Thus, here we empirically assess to what extent the landscape is already overbuilt in the present day in Germany. Therefore, we analyze building locations as they provide the best possible information on built-up areas. Specifically, we apply the City Clustering Algorithm (CCA) and employ the percolation concept in order to quantify the connectivity of buildings. We find that at a critical distance of (830 ± 10) m the building stock in Germany undergoes a transition to a country-spanning building cluster. From this rather short critical distance we infer that the country is covered by a contiguous and dense mesh of buildings. Additionally, we find that the building density decreases as a power-law with an exponent close to 0.75. Complementarily, we identify the sites furthest away from any building. Ironically, the top five largest holes in that mesh are or were military training areas. The largest one corresponds to a radius of only 6.3 km. The results significantly contribute to a deeper understanding of landscape degradation. Settlement connectivity and poles of inaccessibility can serve for monitoring of settlement and landscape changes.