Universal rules for fragmentation of land by humans

The morphology of parcel patterns created by humans both in urban and rural areas is investigated. The parcel size distribution function, f(a), provides a criterion, that enables unambiguous classification of each piece of land as city core, suburbs, or rural area. The morphology of the rural area corresponds to a scale-free structure and follows a power-law distribution f(a) ~ a ⁻ⁿ of the parcel areas with the exponent n ≈ 1. In suburbs, the area distribution follows the log-normal distribution. In the city core, f(a) has an unimodal shape with an algebraically decaying tail, n = 2. Our study is based on data originating mainly from North America, the Hawaiian Islands, and Australia. For the regions analyzed, the characteristics of the parcel size distribution are universal and robust with respect to geographical, historical, and economical conditions accompanying development of a given area. The urbanization process can be described in terms of the changes of the morphology of the patterns of land fragmentation. In this formulation, the rural morphology, which can be thought as natural one because it exhibits a scale-free distribution of parcel sizes, is transformed into the artificial morphology developed in the city centers. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.