IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v140y2020ics0960077920306032.html
   My bibliography  Save this article

Complexity in patterns of racial segregation

Author

Listed:
  • Stepinski, Tomasz F.
  • Dmowska, Anna

Abstract

Cities are complex systems, their complexity manifests itself through fractality of their spatial structures and by power law distributions (scaling) of multiple urban attributes. Here we report on the previously unreported manifestation of urban complexity – scaling in patterns of residential racial segregation. A high-resolution racial grid of a city is segmented into racial enclaves which are patches of stationary racial composition. Empirical PDFs of patch areas and population counts in 41 US cities were analyzed to reveal that these variables have distributions which are either power laws or approximate power laws. Power law holds for a pool of all patches, for patches from individual cities, and patches restricted to specific racial types. The average value of the exponent is 1.64/1.68 for area/population in 1990 and 1.70/1.74 in 2010. The values of exponents for type-specific patches vary, but variations had decreased from 1990 to 2010. We have also performed a multifractal analysis of patterns formed by racial patches and found that these patterns are monofractal with average values of fractal dimensions in the 0.94-1.81 range depending on racial types and the year of analysis. Power law distribution of racial patch sizes and a fractal character of racial patterns present observable and quantifiable constraints on models of racial segregation. We argue that growth by preferential attachment is a plausible mechanism leading to observed patterns of segregation.

Suggested Citation

  • Stepinski, Tomasz F. & Dmowska, Anna, 2020. "Complexity in patterns of racial segregation," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306032
    DOI: 10.1016/j.chaos.2020.110207
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920306032
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110207?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Dongfeng Fu & Fabio Pammolli & S. V. Buldyrev & Massimo Riccaboni & Kaushik Matia & Kazuko Yamasaki & H. E. Stanley, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," Papers physics/0512005, arXiv.org.
    2. Saeedimoghaddam, Mahmoud & Stepinski, T.F. & Dmowska, Anna, 2020. "Rényi’s spectra of urban form for different modalities of input data," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Clémentine Cottineau, 2017. "MetaZipf. A dynamic meta-analysis of city size distributions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-22, August.
    4. Zhijun SONG & Linjun YU, 2019. "Multifractal features of spatial variation in construction land in Beijing (1985–2015)," Palgrave Communications, Palgrave Macmillan, vol. 5(1), pages 1-15, December.
    5. Jean Cavailhès & Pierre Frankhauser & Dominique Peeters & Isabelle Thomas, 2010. "Residential equilibrium in a multifractal metropolitan area," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 45(3), pages 681-704, December.
    6. Chen, Yanguang & Feng, Jian, 2017. "Spatial analysis of cities using Renyi entropy and fractal parameters," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 279-287.
    7. Murcio, Roberto & Rodríguez-Romo, Suemi, 2011. "Modeling large Mexican urban metropolitan areas by a Vicsek Szalay approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(16), pages 2895-2903.
    8. Erez Hatna & Itzhak Benenson, 2012. "The Schelling Model of Ethnic Residential Dynamics: Beyond the Integrated - Segregated Dichotomy of Patterns," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 15(1), pages 1-6.
    9. M. Batty & R. Carvalho & A. Hudson-Smith & R. Milton & D. Smith & P. Steadman, 2008. "Scaling and allometry in the building geometries of Greater London," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(3), pages 303-314, June.
    10. Yamasaki, Kazuko & Matia, Kaushik & Buldyrev, Sergey V. & Fu, Dongfeng & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2004. "Preferential attachment and growth dynamics in complex systems," MPRA Paper 15908, University Library of Munich, Germany, revised 06 Feb 2006.
    11. Eva K. Andersson & Bo Malmberg & Rafael Costa & Bart Sleutjes & Marcin Jan Stonawski & Helga A. G. Valk, 2018. "A Comparative Study of Segregation Patterns in Belgium, Denmark, the Netherlands and Sweden: Neighbourhood Concentration and Representation of Non-European Migrants," European Journal of Population, Springer;European Association for Population Studies, vol. 34(2), pages 251-275, May.
    12. Isabelle Thomas & Marie-Laurence De Keersmaecker & Pierre Frankhauser, 2003. "Using fractal dimensions for characterizing intra-urban diversity. The example of Brussels," ERSA conference papers ersa03p116, European Regional Science Association.
    13. John Logan & Brian Stults & Reynolds Farley, 2004. "Segregation of minorities in the metropolis: two decades of change," Demography, Springer;Population Association of America (PAA), vol. 41(1), pages 1-22, February.
    14. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2018. "Zipf’s law and city size distribution: A survey of the literature and future research agenda," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 75-92.
    15. Lämmer, Stefan & Gehlsen, Björn & Helbing, Dirk, 2006. "Scaling laws in the spatial structure of urban road networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(1), pages 89-95.
    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. Saeedimoghaddam, Mahmoud & Stepinski, T.F., 2021. "Multiplicative random cascade models of multifractal urban structures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    2. Saeedimoghaddam, Mahmoud & Stepinski, T.F. & Dmowska, Anna, 2020. "Rényi’s spectra of urban form for different modalities of input data," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
    4. Jakub Growiec & Fabio Pammolli & Massimo Riccaboni, 2020. "Innovation and Corporate Dynamics: A Theoretical Framework," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(1), pages 1-45, March.
    5. Buldyrev, Sergey V. & Salinger, Michael A. & Stanley, H. Eugene, 2016. "A statistical physics implementation of Coase׳s theory of the firm," Research in Economics, Elsevier, vol. 70(4), pages 536-557.
    6. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2017. "Where Gibrat meets Zipf: Scale and scope of French firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 265-275.
    7. Fernández-Rosales, Iván Yair & Angulo-Brown, Fernando & Pérez-Campuzano, Enrique & Guzmán-Vargas, Lev, 2020. "Distance distributions of human settlements," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    8. Chen, Yanguang, 2013. "A set of formulae on fractal dimension relations and its application to urban form," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 150-158.
    9. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of International Trade," Documents de Travail de l'OFCE 2009-24, Observatoire Francais des Conjonctures Economiques (OFCE).
    10. Anna Dmowska & Tomasz F Stepinski, 2022. "Improving assessment of urban racial segregation by partitioning a region into racial enclaves," Environment and Planning B, , vol. 49(1), pages 290-303, January.
    11. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of Weighted Networks," Papers 0908.0348, arXiv.org, revised Dec 2009.
    12. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
    13. Misako Takayasu & Hayafumi Watanabe & Hideki Takayasu, 2013. "Generalised central limit theorems for growth rate distribution of complex systems," Papers 1301.2728, arXiv.org, revised Jan 2014.
    14. Xie, Wen-Jie & Gu, Gao-Feng & Zhou, Wei-Xing, 2010. "On the growth of primary industry and population of China’s counties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3876-3882.
    15. Jeremy Pais & Scott South & Kyle Crowder, 2009. "White Flight Revisited: A Multiethnic Perspective on Neighborhood Out-Migration," Population Research and Policy Review, Springer;Southern Demographic Association (SDA), vol. 28(3), pages 321-346, June.
    16. Hayato Goto & Eduardo Viegas & Hideki Takayasu & Misako Takayasu & Henrik Jeldtoft Jensen, 2019. "Dynamics of essential interaction between firms on financial reports," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-16, December.
    17. Tse-Chuan Yang & Stephen A Matthews, 2015. "Death by Segregation: Does the Dimension of Racial Segregation Matter?," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-26, September.
    18. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2008. "Are output growth-rate distributions fat-tailed? some evidence from OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 639-669.
    19. Qingxu Huang & Dawn C Parker & Tatiana Filatova & Shipeng Sun, 2014. "A Review of Urban Residential Choice Models Using Agent-Based Modeling," Environment and Planning B, , vol. 41(4), pages 661-689, August.
    20. Thomas Brenner & Matthias Duschl, 2018. "Modeling Firm and Market Dynamics: A Flexible Model Reproducing Existing Stylized Facts on Firm Growth," Computational Economics, Springer;Society for Computational Economics, vol. 52(3), pages 745-772, October.

    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:eee:chsofr:v:140:y:2020:i:c:s0960077920306032. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.