Scaling of geographic space from the perspective of city and field blocks and using volunteered geographic information

Scaling of geographic space refers to the fact that for a large geographic area its small constituents or units are much more common than the large ones. This article develops a novel perspective to the scaling of geographic space using large street networks involving both cities and countryside. Given a street network of an entire country, we decompose the street network into individual blocks, each of which forms a minimum ring or cycle such as city blocks and field blocks. The block sizes demonstrate the scaling property, that is, far more small blocks than large ones. Interestingly, we find that the mean of all the block sizes can easily separate between small and large blocks -a high percentage (e.g., 90%) of smaller ones and a low percentage (e.g., 10%) of larger ones. Based on this regularity, termed as the head/tail division rule, we propose an approach to delineating city boundaries by grouping the smaller blocks. The extracted city sizes for the three largest European countries (France, Germany, and United Kingdom) exhibit power law distributions. We further define the concept of border number as a topological distance of a block far from the outmost border to map the center(s) of the country and the city. We draw an analogy between a country (or a city or geographic space in general) and a complex organism like the human body or the human brain to further elaborate on the power of this block perspective in reflecting the structure or patterns of geographic space.