IDEAS home Printed from https://ideas.repec.org/a/sae/envirb/v48y2021i1p43-59.html
   My bibliography  Save this article

Singularity cities

Author

Listed:
  • Yunfei Li
  • Diego Rybski

    (28412Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Potsdam, Germany)

  • Jürgen P. Kropp

    (28412Potsdam Institute for Climate Impact Research (PIK), Member of the Leibniz Association, Potsdam, Germany; Department of Environmental Sciences & Geography, University of Potsdam, Potsdam, Germany)

Abstract

We propose an upgraded gravitational model which provides population counts beyond the binary (urban/non-urban) city simulations. Numerically studying the model output, we find that the radial population density gradients follow power-laws where the exponent is related to the preset gravity exponent γ . Similarly, the urban fraction decays exponentially, again determined by γ . The population density gradient can be related to radial fractality and it turns out that the typical exponents imply that cities are basically zero-dimensional. Increasing the gravity exponent leads to extreme compactness and the loss of radial symmetry. We study the shape of the major central cluster by means of another three fractal dimensions and find that overall its fractality is dominated by the size and the influence of γ is minor. The fundamental allometry, between population and area of the major central cluster, is related to the gravity exponent but restricted to the case of higher densities in large cities. We argue that cities are shaped by power-law proximity. We complement the numerical analysis by economics arguments employing travel costs as well as housing rent determined by supply and demand. Our work contributes to the understanding of gravitational effects, radial gradients, and urban morphology. The model allows to generate and investigate city structures under laboratory conditions.

Suggested Citation

  • Yunfei Li & Diego Rybski & Jürgen P. Kropp, 2021. "Singularity cities," Environment and Planning B, , vol. 48(1), pages 43-59, January.
  • Handle: RePEc:sae:envirb:v:48:y:2021:i:1:p:43-59
    DOI: 10.1177/2399808319843534
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/2399808319843534
    Download Restriction: no

    File URL: https://libkey.io/10.1177/2399808319843534?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Pierre Frankhauser, 2008. "Fractal Geometry for Measuring and Modelling Urban Patterns," Springer Books, in: Sergio Albeverio & Denise Andrey & Paolo Giordano & Alberto Vancheri (ed.), The Dynamics of Complex Urban Systems, pages 213-243, Springer.
    2. Hernán D. Rozenfeld & Diego Rybski & Xavier Gabaix & Hernán A. Makse, 2011. "The Area and Population of Cities: New Insights from a Different Perspective on Cities," American Economic Review, American Economic Association, vol. 101(5), pages 2205-2225, August.
    3. Brzezinski, Michal, 2014. "Do wealth distributions follow power laws? Evidence from ‘rich lists’," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 155-162.
    4. repec:pri:cepsud:125krueger is not listed on IDEAS
    5. Xavier Gabaix, 2016. "Power Laws in Economics: An Introduction," Journal of Economic Perspectives, American Economic Association, vol. 30(1), pages 185-206, Winter.
    6. DELLOYE, Justin & LEMOY, Rémi & CARUSO, Geoffrey, 2017. "Alonso and the scaling of urban profiles," LIDAM Discussion Papers CORE 2017037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Batten, David F. & Boyce, David E., 1987. "Spatial interaction, transportation, and interregional commodity flow models," Handbook of Regional and Urban Economics, in: P. Nijkamp (ed.), Handbook of Regional and Urban Economics, edition 1, volume 1, chapter 9, pages 357-406, Elsevier.
    8. Levy, Moshe & Solomon, Sorin, 1997. "New evidence for the power-law distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 242(1), pages 90-94.
    9. R'emi Lemoy & Geoffrey Caruso, 2017. "Scaling evidence of the homothetic nature of cities," Papers 1704.06508, arXiv.org.
    10. Daniel Kahneman & Alan B. Krueger & David Schkade & Norbert Schwarz & Arthur A. Stone, 2006. "Would You Be Happier If You Were Richer? A Focusing Illusion," Working Papers 77, Princeton University, Department of Economics, Center for Economic Policy Studies..
    11. Rémi Lemoy & Geoffrey Caruso, 2020. "Evidence for the homothetic scaling of urban forms," Environment and Planning B, , vol. 47(5), pages 870-888, June.
    12. Shandeepa Wickramasinghe & Onyekachukwu Onyerikwu & Jie Sun & Daniel ben-Avraham, 2018. "Modeling Spatial Social Complex Networks for Dynamical Processes," Complexity, Hindawi, vol. 2018, pages 1-12, February.
    13. Andres Gomez-Lievano & HyeJin Youn & Luís M A Bettencourt, 2012. "The Statistics of Urban Scaling and Their Connection to Zipf’s Law," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-11, July.
    14. Daniel Kahneman & Alan B. Krueger & David Schkade & Norbert Schwarz & Arthur A. Stone, 2006. "Would You Be Happier If You Were Richer? A Focusing Illusion," Working Papers 77, Princeton University, Department of Economics, Center for Economic Policy Studies..
    15. A. Stewart Fotheringham & Michael Batty & Paul A. Longley, 1989. "Diffusion‐Limited Aggregation And The Fractal Nature Of Urban Growth," Papers in Regional Science, Wiley Blackwell, vol. 67(1), pages 55-69, January.
    16. Kevin Morgan, 2004. "The exaggerated death of geography: learning, proximity and territorial innovation systems," Journal of Economic Geography, Oxford University Press, vol. 4(1), pages 3-21, January.
    17. Filip Biljecki & Ken Arroyo Ohori & Hugo Ledoux & Ravi Peters & Jantien Stoter, 2016. "Population Estimation Using a 3D City Model: A Multi-Scale Country-Wide Study in the Netherlands," PLOS ONE, Public Library of Science, vol. 11(6), pages 1-22, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Blanchflower, David G. & Oswald, Andrew J., 2008. "Is well-being U-shaped over the life cycle?," Social Science & Medicine, Elsevier, vol. 66(8), pages 1733-1749, April.
    2. Tessa Melkonian & Guillaume Soenen & Maureen Ambrose, 2016. "Will I Cooperate? The Moderating Role of Informational Distance on Justice Reasoning," Journal of Business Ethics, Springer, vol. 137(4), pages 663-675, September.
    3. Varvarigos, Dimitrios, 2011. "Non-monotonic welfare dynamics in a growing economy," Journal of Macroeconomics, Elsevier, vol. 33(2), pages 303-312, June.
    4. Thi Truong An Hoang & Andreas Knabe, 2021. "Time Use, Unemployment, and Well-Being: An Empirical Analysis Using British Time-Use Data," Journal of Happiness Studies, Springer, vol. 22(6), pages 2525-2548, August.
    5. Schwandt, Hannes, 2013. "Unmet Aspirations as an Explanation for the Age U-shape in Human Wellbeing," IZA Discussion Papers 7604, Institute of Labor Economics (IZA).
    6. Gardner, Jonathan & Oswald, Andrew J., 2007. "Money and mental wellbeing: A longitudinal study of medium-sized lottery wins," Journal of Health Economics, Elsevier, vol. 26(1), pages 49-60, January.
    7. Naomi Friedman-Sokuler & Claudia Senik, 2022. "Time-Use and Subjective Well-Being: Is there a Preference for Activity Diversity?," PSE Working Papers halshs-03828272, HAL.
    8. Rémi Lemoy & Geoffrey Caruso, 2020. "Evidence for the homothetic scaling of urban forms," Environment and Planning B, , vol. 47(5), pages 870-888, June.
    9. Leonardo Becchetti & Emanuele Bobbio & Federico Prizia & Lorenzo Semplici, 2022. "Going Deeper into the S of ESG: A Relational Approach to the Definition of Social Responsibility," Sustainability, MDPI, vol. 14(15), pages 1-22, August.
    10. Arnaud Mertens & Philippe Van Kerm, 2023. "Commuting time and absenteeism: Evidence from a natural experiment," LISER Working Paper Series 2023-08, Luxembourg Institute of Socio-Economic Research (LISER).
    11. Deckers Thomas & Falk Armin & Schildberg-Hörisch Hannah, 2016. "Nominal or Real? The Impact of Regional Price Levels on Satisfaction with Life," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 16(3), pages 1337-1358, September.
    12. Lalin Anik & Lara B Aknin & Michael I Norton & Elizabeth W Dunn & Jordi Quoidbach, 2013. "Prosocial Bonuses Increase Employee Satisfaction and Team Performance," PLOS ONE, Public Library of Science, vol. 8(9), pages 1-8, September.
    13. Cid, Alejandro & Ferrés, Daniel & Rossi, Máximo, 2010. "Helping to Unravel the Dynamics of Happiness among the Elderly in the Southern Cone," MPRA Paper 39915, University Library of Munich, Germany.
    14. Alejandro Cid & Daniel Ferres & Máximo Rossi, 2008. "Subjective Well-Being in the Southern Cone: Health, Income and Family," Documentos de Trabajo (working papers) 1308, Department of Economics - dECON.
    15. Christopher Mackie & Conal Smith, 2015. "Conceptualizing Subjective Well-Being And Its Many Dimensions – Implications For Data Collection In Official Statistics And For Policy Relevance," Statistics in Transition New Series, Polish Statistical Association, vol. 16(3), pages 335-372, September.
    16. Wang, Yuanjun & You, Shibing, 2016. "An alternative method for modeling the size distribution of top wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 443-453.
    17. Aaker, Jennifer L. & Garbinsky, Emily N. & Vohs, Kathleen D., 2011. "Cultivating Admiration in Brands: Warmth, Competence, and Landing in the "Golden Quadrant"," Research Papers 2087, Stanford University, Graduate School of Business.
    18. Koen Decancq & Marc Fleurbaey & Erik Schokkaert, 2015. "Happiness, Equivalent Incomes and Respect for Individual Preferences," Economica, London School of Economics and Political Science, vol. 82, pages 1082-1106, December.
    19. Iddisah Sulemana, 2015. "The Effect of Fear of Crime and Crime Victimization on Subjective Well-Being in Africa," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 121(3), pages 849-872, April.
    20. Hilke Brockmann, 2009. "Why Are Middle-Aged People so Depressed?: Evidence from West Germany," SOEPpapers on Multidisciplinary Panel Data Research 233, DIW Berlin, The German Socio-Economic Panel (SOEP).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:envirb:v:48:y:2021:i:1:p:43-59. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.