A gradient model for the spatial patterns of cities

TL;DR

This paper introduces a gradient model that simulates the spatial distribution of city components by balancing gravitational and repulsive forces influenced by city and component attributes, fitting real-world data and revealing underlying self-organizing mechanisms.

Contribution

The paper develops a novel gradient model that quantifies the spatial distribution of multiple city components based on equilibrium of forces, integrating city and component attributes.

Findings

Model accurately fits real-world distribution data for 22 component types.

Reveals a bottom-up self-organizing mechanism in city development.

Predicts distribution curves of city components during urban growth.

Abstract

The dynamics of city's spatial structures are determined by the coupling of functional components (such as restaurants and shops) and human beings within the city. Yet, there still lacks mechanism models to quantify the spatial distribution of functional components. Here, we establish a gradient model to simulate the density curves of multiple types of components based on the equilibria of gravitational and repulsive forces along the urban-rural gradient. The forces from city center to components are determined by both the city's attributes (land rent, population and people's environmental preferences) and the components attributes (supply capacity, product transportability and environmental impacts). The simulation for the distribution curves of 22 types of components on the urban-rural gradient are a good fit for the real-world data in cities. Based on the 4 typical types of components, 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, we predict the distribution curves of many types of components along with the development of cities. The model provides a general tool for analyzing the distribution of objects on the gradients.