Urban Growth and Spatial Structure: Mathematical Models and Empirical Evidence

IT IS well known that the growth of any complex structure is associated with changes in form. The phenomenon is familiar to the biologist, who relates the visible changes of form of a living organism to the differential growth of its parts; it is familiar also to the economist, who recognizes changes in the structure of a growing economy due to the differential growth of its several sectors. If we accept as a point of departure that geography, as both a physical and a social science, is primarily the study of the spatial structure of processes and the resultant spatial structure of phenomena, then the spatial structure of differential growth is an appropriate focus of attention for geographers; for growth and decay are, after all, the measurable expressions of the processes by which the observable spatial structure of any phenomenon at a given point in time is achieved. In this paper the spatial structure of a single spatial process is discussed, namely the differential growth of population density within cities. Certain empirical generalizations about the spatial variation of density in cities and changes in that spatial variation through time are set forth, from which are deduced the rules of intraurban allometric' growth and the density-growth rate relationship. In the manipulation of data within the mathematical framework thus constructed, two urban density constants are tentatively identified, one of which may be of significance in urban planning.