IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v176y2023ics0960077923010925.html
   My bibliography  Save this article

Dynamical fractal: Theory and case study

Author

Listed:
  • Yin, Junze

Abstract

Urbanization is a phenomenon of concern for planning and public health: projections are difficult because of policy changes and natural events, and indicators are multiple. There are previous studies of development that used fractals, but none for this specific problem, nor extrapolating the future trend. In the first part of this paper, we construct a theoretical framework for analyzing dynamic (changing) fractals and extrapolating their future trends based on their fractal dimension—a measure of the complexity of the fractal. We believe this approach holds enormous potential for applications in analyzing changing fractals in the real world, such as urban growth, cells, cancers, etc., all of which are invaluable to research. This theoretical framework may shed light on a factor overlooked in past research: the trend of how fractals change. In the second part of this paper, we apply this theoretical framework to study the urbanization of Boston. We compare several maps and measurements of fractal dimensions, produce code11https://github.com/yinj66/fractal-dimension. that reads the maps and divides the city into subsections, and ultimately graph the fractal dimension over time using both differential and difference equations. Finally, we postulate the logistic equation as a model to fit the evolution of the fractal dimension, as well as the total population derived from census data, which serves as a component for comparing dynamical fractals.

Suggested Citation

  • Yin, Junze, 2023. "Dynamical fractal: Theory and case study," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
  • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010925
    DOI: 10.1016/j.chaos.2023.114190
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923010925
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2023.114190?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. repec:cai:popine:popu_p1998_10n1_0240 is not listed on IDEAS
    2. Dahly, Darren L. & Adair, Linda S., 2007. "Quantifying the urban environment: A scale measure of urbanicity outperforms the urban-rural dichotomy," Social Science & Medicine, Elsevier, vol. 64(7), pages 1407-1419, April.
    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. Shon, Huijoo, 2024. "Urbanicity and child health in 26 sub-Saharan African countries: Settlement type and its association with mortality and morbidity," Social Science & Medicine, Elsevier, vol. 340(C).
    2. Maria E Hermosillo-Gallardo & Russell Jago & Simon J Sebire, 2018. "Association between urbanicity and physical activity in Mexican adolescents: The use of a composite urbanicity measure," PLOS ONE, Public Library of Science, vol. 13(9), pages 1-16, September.
    3. Luca Salvati & Margherita Carlucci, 2020. "Shaping Dimensions of Urban Complexity: The Role of Economic Structure and Socio-Demographic Local Contexts," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 147(1), pages 263-285, January.
    4. Margherita Carlucci & Ilaria Zambon & Luca Salvati, 2020. "Diversification in urban functions as a measure of metropolitan complexity," Environment and Planning B, , vol. 47(7), pages 1289-1305, September.
    5. Van de Poel, Ellen & O'Donnell, Owen & Van Doorslaer, Eddy, 2009. "Urbanization and the spread of diseases of affluence in China," Economics & Human Biology, Elsevier, vol. 7(2), pages 200-216, July.
    6. Falchetta, G. & Noussan, M. & Hammad, A.T., 2021. "Comparing paratransit in seven major African cities: An accessibility and network analysis," Journal of Transport Geography, Elsevier, vol. 94(C).
    7. Carba, Delia B. & Tan, Vivencia L. & Adair, Linda S., 2009. "Early childhood length-for-age is associated with the work status of Filipino young adults," Economics & Human Biology, Elsevier, vol. 7(1), pages 7-17, March.
    8. Finnemann, Adam & Huth, Karoline & van der Maas, Han & Borsboom, Denny & Epskamp, Sacha, 2023. "The Urban Desirability Paradox: UK Urban-rural Differences in Well-being, Social, and Economic Satisfaction," OSF Preprints 3g2d8, Center for Open Science.
    9. Townley, Greg & Brusilovskiy, Eugene & Salzer, Mark S., 2017. "Urban and non-urban differences in community living and participation among individuals with serious mental illnesses," Social Science & Medicine, Elsevier, vol. 177(C), pages 223-230.
    10. E. Van de Poel & O. O'Donnell & E. Van Doorslaer, 2009. "The Health Penalty of China's Rapid Urbanization," Tinbergen Institute Discussion Papers 09-016/3, Tinbergen Institute.
    11. Aiyar, Anaka & Rahman, Andaleeb & Pingali, Prabhu, 2021. "India’s rural transformation and rising obesity burden," World Development, Elsevier, vol. 138(C).
    12. Okoruwa, V. & Ikudayisi, A., 2018. "Urbanization and Food Security: Empirical Evidence from Households in Urban Southwest Nigeria," 2018 Conference, July 28-August 2, 2018, Vancouver, British Columbia 277053, International Association of Agricultural Economists.
    13. Marion Gouin & Cyril Flamant & Géraldine Gascoin & Valérie Rouger & Agnès Florin & Philippe Guimard & Jean-Christophe Rozé & Matthieu Hanf, 2015. "The Association of Urbanicity with Cognitive Development at Five Years of Age in Preterm Children," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-15, July.
    14. Davis, Brennan & Grier, Sonya, 2015. "A tale of two urbanicities: Adolescent alcohol and cigarette consumption in high and low-poverty urban neighborhoods," Journal of Business Research, Elsevier, vol. 68(10), pages 2109-2116.
    15. Adair, Linda S. & Carba, Delia B. & Lee, Nanette R. & Borja, Judith B., 2021. "Stunting, IQ, and final school attainment in the Cebu Longitudinal Health and Nutrition Survey birth cohort," Economics & Human Biology, Elsevier, vol. 42(C).
    16. Madjid Atek & Pierre Traissac & Jalila El Ati & Youcef Laid & Hajer Aounallah-Skhiri & Sabrina Eymard-Duvernay & Nadia Mézimèche & Souha Bougatef & Chiraz Béji & Leila Boutekdjiret & Yves Martin-Préve, 2013. "Obesity and Association with Area of Residence, Gender and Socio-Economic Factors in Algerian and Tunisian Adults," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-10, October.
    17. Harini Nagendra & Hita Unnikrishnan & Sreerupa Sen, 2013. "Villages in the City: Spatial and Temporal Heterogeneity in Rurality and Urbanity in Bangalore, India," Land, MDPI, vol. 3(1), pages 1-18, December.
    18. Abay, Kibrom A. & Amare, Mulubrhan, 2018. "Night light intensity and women’s body weight: Evidence from Nigeria," Economics & Human Biology, Elsevier, vol. 31(C), pages 238-248.
    19. Chamara P. Liyanage & Koichi Yamada, 2017. "Impact of Population Growth on the Water Quality of Natural Water Bodies," Sustainability, MDPI, vol. 9(8), pages 1-14, August.
    20. Zachary Zimmer & Luoman Bao & Nanette L. Mayol & Feinian Chen & Tita Lorna L. Perez & Paulita L. Duazo, 2017. "Functional limitation trajectories and their determinants among women in the Philippines," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 36(30), pages 863-892.

    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:176:y:2023:i:c:s0960077923010925. 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.