ArticleJournal of the Royal Society, Interface2021
How the geometry of cities determines urban scaling laws.
Article in Journal of the Royal Society, Interface, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 17 papers, 1 of them a synthesis that pooled it.
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Who cites it
17 citing papers in PubMed, 1 synthesis or guideline pooled it.
- Recent advances in urban system science: Models and data.PloS one · 2022Pooled it
- Scaling laws for function diversity and specialization across socioeconomic and biological complex systems.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Intra-settlement scaling across the urban-rural continuum: material stocks, service provisioning, and greenhouse gas emissions in the contiguous United States.Journal of industrial ecology · 2026Article
- The emergence of urban scaling in Ancient Southwest Asia.PloS one · 2026Article
- Unraveling urban dynamics: Scaling laws of human mobility across the cityscape divide.Fundamental research · 2025Article
- A stochastic theory of urban metabolism.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Exploring the interplay between population profile and optimal routes in U.S. cities.Scientific reports · 2025Article
- Urban Scaling Functions: Emission, Pollution and Health.Journal of urban health : bulletin of the New York Academy of Medicine · 2024Article
- Implicit racial biases are lower in more populous more diverse and less segregated US cities.Nature communications · 2024Article
- The dynamic resilience of urban labour networks.Royal Society open science · 2023Article
- Scaling of the morphology of African cities.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Article
- Prospective for urban informatics.Urban informatics · 2022Article
- Urban spatial form analysis based on the architectural layout -- Taking Zhengzhou City as an example.PloS one · 2022Article
- Non-trivial relationship between scaling behavior and the spatial organization of GDP in Indonesian cities.PloS one · 2022Article
- The structure, centrality, and scale of urban street networks: Cases from Pre-Industrial Afro-Eurasia.PloS one · 2021Article
- The effect of dragon-kings on the estimation of scaling law parameters.Scientific reports · 2020Article
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Authors and funding
2 authors.
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No grant is acknowledged in the PubMed record.
Abstract
Urban scaling laws relate socio-economic, behavioural and physical variables to the population size of cities. They allow for a new paradigm of city planning and for an understanding of urban resilience and economics. The emergence of these power-law relations is still unclear. Improving our understanding of their origin will help us to better apply them in practical applications and further research their properties. In this work, we derive the basic exponents for spatially distributed variables from fundamental fractal geometric relations in cities. Sub-linear scaling arises as the ratio of the fractal dimension of the road network and of the distribution of the population embedded in three dimensions. Super-linear scaling emerges from human interactions that are constrained by the geometry of a city. We demonstrate the validity of the framework with data from 4750 European cities. We make several testable predictions, including the relation of average height of cities and population size, and the existence of a critical density above which growth changes from horizontal densification to three-dimensional growth.
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