A Systematic Review of Fractal Theory and its Application in Geography and Urban Planning
Keywords:
Fractal Theory; Systematic Review; Content Analysis; Measures and Measurement Method; Urban PlanningAbstract
Fractal has been considered as an optimized structure of nature and an effective tool for depicting spatial complexity. A city can be deemed as a fractal system with self-similarity, and are, therefore, ideal candidates for fractal analysis. Recent decades have witnessed great strides in research on fractal cities in various aspects of urban forms and structures as well as urban development dynamics. Considering the deep and wide-ranging applications of fractal theory in explaining local and spatial complexities, this study aimed at conducting a systematic review and content analysis of research conducted on fractal in order to pinpoint practical and theoretical frameworks they can provide to specialists in the fields of geography and urban planning. To this end, a systematic review was carried out in three general stages of study selection, evaluation, and synthesis of findings. Results showed that developing and emerging concepts in theoretical and experimental studies, which has sought to explain the roles and applications of fractal theory in research and simulations of the built environment could be classified in 10 areas of psychology, architecture, urban design, urban form and structure, urban boundary shape, land use, urban traffic, urban growth modeling, urban hierarchy, and benefits of fractals. Studies related to urban form and structure (N= 37) accounted for the largest share of studies. In addition, key methods leading to the development of fractal studies in the existing literature were use of fractal dimension and Hausdorff dimension (34%), boundary dimension (24%), and network or box-counting dimension (14%) followed by power law (PL) distributions, power laws, and power-scale law (7%).
References
Aliakbari, E., Taleshi, M., & Emad al-Din, A. (2017). An integrated model for physical development of cities and their periphery using the tourism capacities of urban areas. Physical Development Planning, second year, number 1, consecutive 5, 9-24.
Ana-Maria, Ciobotaru Ion Andronache, Nilanjan Dey, Martina Petralli, Mohammad Reza Mansouri Daneshvar, Qianfeng Wang, Marko Radulovic, Radu-Daniel Pintilii (2018). Temperature-Humidity Index described by fractal Higuchi Dimension affects tourism activity in the urban environment of Focşani City (Romania). Theoretical and Applied Climatology, 133, 1-11.
Batty, M. (2005). Cities and Complexity: Understanding Cities with Cellular Automata, Agent-Based Models, and Fractals. London, England: The MIT Press.
Batty, M. (2008). The size, scale, and shape of cities. Science, 319, 769-771.
Batty, M., Fotheringham, A.S., & Longley, P. A. (1989). Urban growth and form: scaling, fractal geometry and diffusion-limited aggregation. Environmental Planning A, 21, 1447–72.
Batty, M., & Longley, P. A. (1994). Fractal Cities: A Geometry of Form and Function. London: Academic Press
Blanco, R., & José, J. (2019). The fractal geometry of Luhmann's sociological theory or debugging systems theory. Technological Forecasting & Social Change, 146, 31–40, https://doi.org/10.1016/j.techfore.2019.05.020.
Bovill, C. (1996). Fractal Geometry in Architecture and Design. Springer.
Chen, Y., Wang, Y., & Li, X. (2019). Fractal dimensions derived from spatial allometric scaling of urban form. Chaos, Solitons and Fractals 126, 122–134, https://doi.org/10.1016/j.chaos.2019.05.029.
Chen, Y., & Feng, J. (2017). Spatial analysis of cities using Renyi entropy and fractal parameters. Chaos, Solitons and Fractals, 105, 279–287, https://doi.org/10.1016/j.chaos.2017.10.018
Chen, Y. (2011). Derivation of the functional relations between fractal dimension of and shape indices of urban form. Computers, Environment and Urban Systems, 35, 442–451, doi:10.1016/j.compenvurbsys.2011.05.008
Chen, Y. G. (2008). A wave-spectrum analysis of urban population density: entropy, fractal, and spatial localization. Discrete Dynamics in Nature and Society, Article ID 728420, 22 pages.
Chen, Y., & Zhou, Y. (2004). Multi-fractal measures of city-size distributions based on the three-parameter Zipf model. Chaos, Solitons and Fractals, 22, 793–805, doi:10.1016/j.chaos.2004.02.059
Chen, Y. (2015). The distance-decay function of geographical gravity model: power law or exponential law?” Chaos, Solitons & Fractals, 77, 174–189.
Dietzel, C., Herold, M., Hemphil, J. J., & Clarke, K. C. (2005). Spatio-temporal dynamics in California's central valley: Empirical link to urban theory. International journal of geographical information science, 19(2), 175- 195.
Feng, Y., & Liu, Y. (2015). Fractal dimension as an indicator for quantifying the effects of changing spatial scales on landscape metrics. Ecological Indicators, 53, 18–27, http://dx.doi.org/10.1016/j.ecolind.2015.01.020.
Frankhauser, P., & Sadler, R. (1991). Fractal analysis of agglomerations. In: Natural Structures: Principles, Strategies, and Models in Architecture and Nature. Ed. M. Hilliges. Stuttgart: University of. Stuttgart, pp 57-65.
Ghadiri, M., & Khoshnood, F. (2018). An Analysis of the pattern of and factors affecting Abadan spatial expansion. Geographical Space Quarterly, 1(2), 1-4.
Gharakhloo, M., & Zanganeh Shahraki, S. (2009). Recognition of the physical-spatial growth patterns of a city using quantitative models, a case study of Tehran. Journal of Geography and Environmental Planning, No. 1.
Goodarzi, Gh., & Haghani, T. (2016). Study of urban context dispersion using fractal geometry model and complexity theory to find urban development patterns in Tehran's 20th district. Journal of Modeling in Engineering, Semnan University, 13(43), 79-89.
Heidari, M. J., & Shokouhi, A. (2016). A comparative study of morphology of old and new urban contexts based on fractal model: the case of selected neighborhoods in old and new contexts of Zanjan. Journal of Urban Areas Studies, Shahid Bahonar University of Kerman, Third Year, (1), 39-61.
Ivanovici, M., & Richard, N. (2010). Fractal dimension of color fractal images. IEEE Trans Image Process, 20(1), 227–35.
Ku, S., Lee, Ch., Chang, W., & Song, J. W. (2020). Fractal structure in the S&P500: A correlation-based threshold network approach. Chaos, Solitons and Fractals, 137, 109848, https://doi.org/10.1016/j.chaos.2020.109848.
Li, J., Du, Q., & Sun, C. (2009). An improved box-counting method for image fractal dimension estimation. Pattern recognition, 42(11), 2460-2469.
Li, H., Wei, H. D., & Korinek, K. (2018). Modelling urban expansion in the transitional greater Mekong region. Urban Studies, 55(8), 1729-1748.
Lu, X., Clements-Croome, D., & Viljanen, M. (2012)a. Fractal geometry and architecture design: case study review. Chaotic Model. Simul. (CMSIM), 311–322.
Lu, X., Clements-Croome, D., & MarttiViljan, M. (2012)b. Fractal Geometry and Architecture Design: Case Study Review.
Madani Isfahani, F. (2011). Urban space design, an intervention in a complex system with emphasis on geometric fractal dimensions in the urban landscape. Master’s Thesis, School of Architecture and Urban Design, Isfahan University of Arts.
Mandelbrot, B. (1977). Fractals, Form, Chance and dimension. San Francisco: Freeman.
Mandelbrot, B. (1983). The Fractal Geometry of Nature. New York: W. H. Freeman and Company
Mandelbrot, B. (1989). Fractal geometry: what is it, and what does it do? Proceedings of the Royal Society of London A: Mathematical and Physical Sciences, 423, 3-16.
Meredian, A. (2018). Double Exposure and Fractal City: Cultural Disengagement and Disembodied Belonging due to Outdoor Thermal Changes. Journal of Regional and City Planning, 29, 67-82.
Mirkatouli, J., Bargahi, R., & Aghili, S. Z. (2014). Explaining different aspects of using fractal geometry in geographical analysis and urban planning. Geographical Planning of Space, 4(14), 55-82.
Mohajeri, N. (2007). Fractal city, the language of nature in urban design. PhD Thesis, Islamic Azad University, Science and Research Branch.
Mohajeri, N. (2008). Physical stability in traditional Iranian cities, principles of coherence and complexity in urban design - fractal structures. Environmental Technology Quarterly, 10(3), 121-129.
Mohajeri, N. (2012). Effects of external constraints on the general shape and internal geometric patterns of cities. Ph.d thesis, Department of geography and Centre for advanced spatial Analysis, University College London.
Parker, D. C., Manson, S. M., Janssen, M. A., Hoffmann, M. J., & Deadman, P. (2003). Multi-agent systems for the simulation of land-use and land-cover change: a review. Annals of the Association of American Geographers, 93(2), 314–337.
Sala, N. (2003). Fractal Geometry and Self-Similarity in Architecture: An Overview across the Centuries. Isama bridge conference.
Salingaros, N. A. (2006). Compact city replaces sprawl. chapter in: crossover: architecture, urbanism, technology, edited by Arie Graafland and Leslie Kavanaugh.
Salingaros, N. A. (2005). Principles of Urban Structure. Techno Press, Amsterdam, Holland.
Smeed, R. J. (1963). Road development in urban area. Journal of the Institution of Highway Engineers, 10(1), 5-30.
Thomas, I., Frankhauser, P., & Biernacki, C. (2008). The morphology of built-up landscapes in Wallonia (Belgium): A classification using fractal indices. Landscape and Urban Planning, 84(2), 99-115.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
