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Computing the Urban Sprawl Dynamics through Fractal Geometry

Nisar Ali


Urban sprawl has become a very magnificent topic throughout the world since last decade. Various techniques, methodologies and quantitative approaches are based to measure urban sprawl in previous researches. In this research a different idea of fractal analysis is introduced to analyze the urban sprawl. In addition density gradient and sprawl index techniques have also been used to characterize the urban sprawl in Karachi. In this study, we have discussed the urban sprawl of Karachi from its first census (1951) to 2012. Massive flight of the population is recorded between 1981 and 1998 to the periphery of city Karachi. As a result central population density decreased at rapid space and population density gradient exhibits a gentle slope. Overall population density of Karachi constantly increases from 1951 to 1998 but it decreases in 2012 because large rural lands were converted into urbanized lands during 2002 to 2012. For the same six time periods, urban form of Karachi is also quantified through fractal analysis in the context of urban sprawl dynamics. Our results suggest that the fractal dimension of urban form is proportional to the urban sprawl index for the concentrated urban growth patterns. We have also tried investigating sprawl phenomena theoretically further, we have probed the causes and impacts of urban sprawl in Karachi in a given time periods.

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Miron RJ (2003), “Urban sprawl in Canada and America just how dissimilar”, Social Science and Humanities Research Council, Canada.

Burchell R, Downs A, Listokin D, Phillips HS, Seskin S, Shadet NA (1998), “The Cost of Sprawl- Revisited”, National Academy Press, Washington, D.C.

Downs A (1999), “Some Realities About Sprawl And Urban Decline”, Housing Policy Debate, Volume 10, pp. 955−974.

Brueckner JK (2000), “Urban Sprawl: Diagnosis and Remedies”, International Regional Science Review, Volume 23, Issue 2, pp. 160−171.

Hall P (1996), “Cities of Tomorrow”, Blackwell, New York.

Batty M, Longley P (1994), “Fractal Cities”, Academic Press, London.

Torrens PM, Alberti M (2000), “Measuring Sprawl”, Working Paper Series, CASA- Centre for Advanced Spatial Analysis, University College London, London.

Malpezzi S, Guo WK (2001), “Measuring Sprawl: Alternative Measures of Urban Form In U.S. Metropolitan Areas”, The Center for Urban Land Economics Research, University of Wisconsin, Madison, WI.

Ewing R (1997), “Is Los Angeles-Style Sprawl Desirable”, Journal of the American Planning Association, Volume 63, Issue 1, pp. 107–126.

Shen G (2002), “Fractal dimension and fractal growth of urbanized areas”, Int. J. Geographical Information Science, Taylor & Francis Ltd.

Ewing R, Pendall, R, Chen D (2002), “Measuring Sprawl and Its Impact”, Smart Growth America, Washington DC

Bertalanffy L (1968), “General System Theory”, Allen Lane the Penguin Press, New York.

Klir GJ (1972), “Trends in General Systems Theory”, John Wiley and Sons, Inc, New York.

Batty M, Xie Y (1996), “Fractal Cities”, Academic Press, London.

Mehaffy MW, Salingaros NA (2001), “Geometrical Fundamentalism”, Available from www.sphere.,

Shakila R (1983), “Population Densities within Karachi City”, M.Phil thesis, Department of Geography, University of Karachi, Pakistan,

Akhtar S, Dhanani MR, “Population distribution in Karachi city”, Sindh University Research Journal (Science Series), Pakistan, 2013.

Pieser RB (1989), “Density and Urban Sprawl”, Land Economics, Volume 65, pp. 193−204.

Gordon P, Richardson HW, “Are Compact Cities A Desirable Planning Goal”, Journal of the American Planning Association, Volume 63, Issue 1, pp. 95–106.

Peitgen HO, Jurgens H, Saupe D (1997), “Chaos and fractals”, New Frontiers of Science, Sproinger- Verlag Press, New York,

Mandelbrot BB (1983), “The Fractal Geometry of Nature”, Freeman, New York,

Trezi F, Serdar Kaya H (2008), “Analyzing urban sprawl fatterns through fractal geometry: the case if Istanbol metropolitan area”, Centre for Advanced Spatial Analysis, University College London,

Chen Y (2010), “Exploring the Fractal Parameters of Urban Growth and Form with Wave-Spectrum Analysis”, Beijing, China,

Thomas , Frankhauser P, Frenay B, Verleysen M, “Clustering patterns of urban built-up areas with curves of fractal scaling behavior”, Belgium.

Bertaud A, Malpezzı S (1999), “The Spatial Distribution of Population in 35 World Cities: The Role of Markets, Planning and Topography”, Center of Urban Land Economics Research, The University of Wisconsin, WI, USA,

Clark C (1951), “Urban Population Densities”, Journal of Royal Statistical Society, Volume 114, Issue 2, pp. 121−134.


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