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The dynamics of city's spatial structures are determined by the coupling offunctional components (such as restaurants and shops) and human beings withinthe city. Yet, there still lacks mechanism models to quantify the spatialdistribution of functional components. Here, we establish a gradient model tosimulate the density curves of multiple types of components based on theequilibria of gravitational and repulsive forces along the urban-ruralgradient. The forces from city center to components are determined by both thecity's attributes (land rent, population and people's environmentalpreferences) and the components attributes (supply capacity, producttransportability and environmental impacts). The simulation for thedistribution curves of 22 types of components on the urban-rural gradient are agood fit for the real-world data in cities. Based on the 4 typical types ofcomponents, the model reveals a bottom-up self-organizing mechanism that is,the patterns in city development are determined by the economic, ecological,and social attributes of both cities and components. Based on the mechanism, wepredict the distribution curves of many types of components along with thedevelopment of cities. The model provides a general tool for analyzing thedistribution of objects on the gradients.

A gradient model for the spatial patterns of cities