Computing the Urban Sprawl Dynamics Through Fractal Geometry

Journal of Controller and Converters Volume 4 Issue 3

Computing the Urban Sprawl Dynamics through Fractal Geometry

Nisar Ali Ph.D. Scholar, Department of Mathematical sciences, Federal Urdu University of Arts, Science & Technology, Karachi, Pakistan Email: [email protected] DOI: http://doi.org/10.5281/zenodo.3426853

Abstract 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.

Keywords: Density gradient, form, fractal analysis, fractal dimension, quantitative approach, urban sprawl

INTRODUCTION and large fiscal distinctions among Urban sprawl was initially identified in individual communities [2−4]. America during 1950s, when it was observed that population density of cities Urban sprawl and population dispersal in declined [1] and urban areas expanded Karachi city are associated with the rapid with faster rate than population growth population growth and sudden areal rate. Urban researchers coined a term growth, government policies of population “urban sprawl” for this phenomenon. A dispersal and horizontal/linear growth and clear and precise definition of Urban huge conversion of urbanized lands/areas. sprawl is absent yet. Urban sprawl is a In develop countries like United States term associated with the rapid growth of (US), Canada and United Kingdom (UK) urban area resulted loss of agricultural etc., urban sprawl is related with fast land, forest and rangeland leapfrog and expansion of suburbans. In the United commercial strip development. Other States and the United Kingdom essential features of sprawl consist of suburbanization initiated in the early 20th infinite outward extension of development, century as a result of the strategies of dominance of transportation by private population de-concentration and industrial automobiles, fragmentation of land use, decentralization [5], because of fast suburbanization the central population

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dencity slope downed while population disorganized and can be stated as complex density gradient got gentle. While structure. Complex systems approaches measuring sprawl the most important behave the urban areas as dynamic, factor is the density which is a very nonlinear, dissipative, open structures [12, difficult concept because its measures vary 13]. in many ways, so it is quite worthy to clarify certain points. An alternative Euclidean geometry nearly fails to explain approach to quantifying density instead of the highly complex spatial organization, using the dwelling units per given area or but fractal analysis offers different number of people is the density approaches on the urban landscape that gradient.zzc [6−8]. Urban dynamics cause takes into account urban spatial cities grow and economies develop can be complexity [6, 14, 15]. Fractal geometry illustrated by the gradient models which and Chaos theory provide a comprehensive generalizes urban form as mono-centric. idea to understand urban development in [8]. Built sspace in urban areas is the space.complex systems and the complexity additional feature of sprawl configuration. level of morphological differences are The spatial configuration provides more undergone through Chaos theory and blueprints than the size or geometry of fractal geometry repectively. cities. These features increase the rate of the spatial expansion of metropolitan areas PREVIEW TO THE DEVELOPMENT by generating discontinuous land use PROCESS OF KARACHI patterns [9, 10] identified the dimensions Sprawling urban development in many of sprawl i.e. density, continuity, metropolitan areas throughout the world concentration, compactness, centrality, has become a very hot topic since last nuclearity, diversity, and proximity and decade and the associated conversion of latter Ewing R, [11] also generated a rural land into urban land is the similar sprawl index based on four factors that can important issue as well. Karachi being the be measured and analyzed: largest city in Pakistan facing the same important issue as its urban development  Residential density and population is increasing day by day. In  Neighborhood mix of homes, jobs, and the United States of America (USA), most services, of citizens like independent housing with  Strength of activity centers and open space rather than apartments, downtowns, and however suburban residents worry about  Accessibility of the street networks. the increasing commuting cost [5]. In the less developed countries, where percentage The density of the urban centre would rise of urban population is low and during urbanization and the population suburbanization has not achieved desired would remain heavily concentrated in the results, urban sprawl is quite important city centre with a rapid decline in problem in the mega city like Karachi settlement towards the periphery. With this especially in the absence of proper urban ongoing enhancement in economy and the infrastructure like water supply, sewerage network expansion in public transports system, mass transit, and transportation many residents would then gradually shift means. Urban growth in Karachi is towards the suburbs, which cause the different from Western cities where suburban growth is an important feature of gradual softness in density gradient of sprawl. Therefore, it is important to work population. This evidence can be seen in on spatial pattern of population Table 5 in our present case study of distribution and density gradient patterns Karachi urban sprawling. This evidence in Karachi. Karachi city started its growth that the urban development process is

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as recognized city from 1729 with the suburbanization and retail expansion estimated population of 1000 and area of patterns in the metropolitan areas. This 0.12 [16]. According to the census of enhancement in accessibility affected the 1951, the population of Karachi increased location of the new residential settlements to 1.6 million while in 1941 it was and the location of firms as well. The estimated 386,655 with area 115 (Census construction of huge residential apartments, 1951). This rapid enhancement in the shopping malls, elite educational institutes, population occurs soon after the creation modern towns and industries has caused the of Pakistan in 1947 because Karachi was outward expansion of the city. Due to this chosen as the first capital of the country. expansion and suburbanization movement, And soon after the independence almost 1 new sub-centers have emerged and this million people came to Karachi from India multi-center development has been thus rapid population growth and areal encouraged and supported. Thus, Karachi expansion of city took place. This rapid has been divided into 6 districts and 18 growth of the city has affected urban towns. The continuous population growth spatial development. Which lead to lessen with result of multi-centered peripheral the density gradient 1.37 to 1.16 during development has dominated the 1931 and 1951 repectively [17]. According development characteristic of the city to the census of 1961 its population Karachi. The recent housing schemes like increased to almost 1.9 million, while in Steel Town, Gulshan-e-Memar, DHA 1972 it reached to 3.4 million with an area Housing city and Behria Town has of 640 (census 1972). The population expanded the peripheral area of city more. growth and areal growth of Karachi did Such rural lands around Karachi City have not stop and it continued to increase. been converted for planned and unplanned housing, squatter settlements and factories Unlimited new housing projects like Taiser etc. Rapid conversion of rural land into Town, Khuda Ki Basti, Halkani, Shah urban land uses had been taking place during Latif Town were developed as well as the last decade (2002 to 2012). The many new squatter settlements were built construction of new flyovers had played an in peripheral land of the city. Population of important role in the sprawl of city. It is also peripheral residential areas which were observed that due to the development in developed in 1980s like Gulistan-e-Jauhar, economic conditions of people of the city North Karachi, GulzareHijri, Surjani, unlimited private cars, automobiles and Baldia and Orangi had increased monocycles had increased significantly significantly [17]. The 1981 census while on the other hand due to rapid recorded its population 5,153,000 and the enhancement in population number of public 1998 census recorded 9,280,000 transport like mini buses, green buses, vans, respectively. That means the city had rakshaws were introduced. This rapid grown about double of its population development/increase of vehicles during 17 years. In 2010 population of encourages population dispersal and sprawl. Karachi was estimated 15 million and its Such developments in Karachi result sharp area extended to about 1,200. We observed decline in the center population density that initially Karachi had low density and gradient and population density as well informal residential areas were located at (Table 5). the periphery which accelerated the expansion of Karachi. Because of this DATA AND METHODOLOGY sprawlness, illegal and unorganized Quantification of urban sprawl patterns are residential areas have started to invade the based on two variable density and proximity, water basins, forests and high quality which are considered basic components of agricultural land. In addition, construction of measuring urban sprawl [1, 18, 19, 25]. bridges, central roads and peripheral Density is the variable which is defined in highways had a significant impact on

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many ways. It is the ratio between built up time. It calculates the amount of residential area and total area, persons or dwellings per area per person and assists us to define the hectare is also known as density OR number type of development either sprawling or of people inhabiting in an urbanized area. compact. Gross neighborhood densities are Here we have considered density and determined using built up area by the proximity as the variables in the calculation census records. of the sprawl index keeping in mind the development of population and expansion of The second property of the sprawl index Karachi city since last six decades is “proximity” as we have defined (1951−2012). Using the sprawl index, it is earlier. Proximity provides the extent of intended to calculate the urban sprawl pattern population concentration of of city over time and for this purpose we have neighborhoods to the city center. examined the urban spatial development Basically, it determines the position of a pattern by fractal analysis to characterize built up area near or far from the center urban sprawl complexity within the opted of the city. Being multi-centered city, time period. The data has been taken from the Karachi possesses multi-development census record of 1951, 1961,1972,1981,1998 characteristics. In our study we have and estimate data of 2005, respectively. used a new approach to calculate the Using GIS techniques, 178 Union Councils “proximity”. We have considered the (UC’s) of 18 towns have been classified and Central District (CD) as the centre of these 178 neighborhoods were clipped to the city because it is the most dense district built up areas which have been taken as the of Karachi in which four towns are statistical units for the calculation of sprawl included those are Liaqat Abad Town, index. Further we have made/suggested a North Nazimabad Town, Gulberg Town better/suitable division of city either in district and New Karachi town. The distance to wise or town wise. the Central District (CD) and sub- centers have been calculated separately Calculation of Sprawl Index and Sprawl for the East, West and South(Arabian Measurement Sea Side) sides of Karachi and weighted “Population density” is the initial in accordance with the organized gross component of Sprawl Index. Population leasable retail area of each district density basically gives the way to (Table 1, 2 and 3). determine the populated land use over

Table 1: East side. Sr. No. Towns Total gross leasable area % Weight 1 CD 2,286,764 0.62 0.62 2 Jamshed Town 733,821 0.20 0.20 3 Gulshan Town 646,662 0.18 0.18 4 Total 3,667,247 1.00 1.00 Source: Census Record of Pakistan (1998)

Table 2: West side. Sr. No. Districts Total gross leasable area % Weight 1 CD 2,286,764 0.59 0.59 2 S.I.T.E Town 467,560 0.12 0.12 3 Orangi Town 723,694 0.19 0.19 4 Baldia Town 406,165 0.10 0.10 5 Total 3,884,183 1.00 1.00 Source: Census Record of Pakistan (1998).

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Table 3: South side (Arabian sea side). Sr. No. Districts Total gross leasable area % Weight 1 CD 2,286,764 0.58 0.58 2 Lyari Town 607,992 0.16 0.16 3 Saddar Town 616,151 0.16 0.16 4 Kemari Town 383,778 0.10 0.10 5 Total 3,894,685 1.00 1.00 Source: Census Record of Pakistan (1998)

(Now we calculate the from the census record of 1998. This Accumulated/combined distance to CD gives us perfect results for all from all sides. The data has been taken parameters)

Table 4: East, west, and south side. Sr. No. Districts Gross leasable area % Weight 1 CD 2,286,764 0.33 0.33 2 Jamshed Town 733,821 0.11 0.11 3 Gulshan Town 646,662 0.09 0.09 4 S.I.T.E Town 467,560 0.07 0.07 5 Orangi Town 723,694 0.11 0.11 6 Baldia Town 406,165 0.06 0.06 7 Lyari Town 607,992 0.09 0.09 8 Saddar Town 616,151 0.09 0.09 9 Kemari Town 383,778 0.05 0.05 6,872,587 10 Total 1.00 1.00

Source: Census Record Pakistan (1998)

(Table 4) In 1998, there were 16 towns in The sprawl index combines ‘density’ and the city therefore the weight of CD has ‘proximity to centers’ which exhibit been taken as 0.33 in the calculation of inverse effect in the context of urban proximity score, while the weight of the sprawl measurement, so the proximity sub-centers like; Jamshed Town, Gulshan factor is assumed as a negative component. Town, S.I.T.E Town, Orange Town, The sprawl index was calculated by usin Baldia Town, Lyari Town, Sadder Town the following expressions: and Kemari Town as 0.11,0.09,0.07,0.11,0.06,0.09,0.09 and

0.05 respectively. After 1998, the multi- centered characteristics of city increased ( ) ( ) and another sub-centers (towns) on different sides emerged. There for the ( ) weight of CD has been changed as 0.24 (calculated using estimated data of 2005) in the calculation of proximity score, while Where, the weight of Jamshed Town, Gulshan Sprawl index for year “n” Town, S.I.T.E Town, Orange Town, : Standarized values of gross Baldia Town, Lyari Town, Sadder Town population density of a neighbourhood and Kemari Town has been assumed as : Sum of standardized values of 0.08,0.07,0.05,0.08,0.04,0.06,0.07 and geographic distance to a neighbourhood to 0.04 respectively. the CD, and rest of all subcenters

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...: Weights of the city (2) A compact neighborhood is the one centers of the CD, and sub centers. which score sprawl value defined by 1 The standardized values of “population standard deviation above the mean of the density” and “proximity to center” were sprawl index and if the value is within an combined to determine the overall Sprawl interval of 1 standard deviation of the Index, this scale is based on: (1) A mean of sprawl index, it is represented as a Sprawled neighborhood is the one which neighborhood in transition that means this score sprawl value defined by 1 standard neighborhood neither sprawling nor deviation below the mean of sprawl index. compact (Fig. 2).

Figure 1: Evaluation of overall sprawl scores.

Urban sprawl through population is the population density at distance density ‘y’ from city center. Now we compute the central population ’ is the central density, ‘b’ is a density ( ) and population density population density gradient, gradient (b) by using the census and ‘y’ is distance from city center and ‘e’ is estimated data (1951-1998, 2012) to get natural log. further evidence of urban sprawling in Karachi. We have used the Model of Clark Surely urban sprawling exhibits when an [26] which was found best fitted to urbanized area grows at a rapid space than investigate the pattern of population the population growth rate. In 1951, large density distribution of Karachi city. population and areal growth rate is According to this model the population experienced mainly due to mass migration density exponentially declines with from India and rest of the Pakistan. increasing distance from the city centre. However, during that era urban areal Mathematically, it is modeled as following growth rate was also lower than population expressions: growth rate. But in 2012, our computed

results show higher urbanized a real Where, growth rate than the population growth

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rate for the first time (Table 5) which is These results of both declining population perhaps the cause of significant number of density and higher rate of growth of populations moved from FATA and Swat urbanized area in 2012 confirm the to Karachi as a result military operation sprawling of Karachi city with constant (Zarb-e-Azab) against the terrorist wings. pace (Fig. 4 (a), 4 (b)).

1951, 12.612

1972, 11.652

1962, 11.983 1998, 10.301 1981, 11.541 10

2012, 8.889

5 1950 1960 1970 1980 1990 2000 2010

Figure 2: Distance from the city center data is placed on x-axis and log population density (Ln ) on y-axis. (1951-1998, 2012).

Table 5: Census wise data and estimated data (2012) calculations. Central Total population Growth rate of Population density Central Density Census density. urbanized area growth rate density gradient (Year) (person per sq. (percentage) (percentage) (person per (Log ) (b) km) sq.km) 1951 4145 12.197 14.200 300228 12.612 -1.16211 1961 4259 1.534 1.785 160075 11.983 -0.69845 1972 5466 3.201 5.490 114955 11.652 -0.45542 1981 6134 3.022 4.302 102867 11.541 -0.37101 1998 7733 2.098 3.460 29747 10.301 -0.19558 2012 7258 3.648 3.412 7258 8.889

Table 6: Distance-wise population density distribution in Karachi City, 1981. Distance from the city Population density Distance from the Population density Centre (km) (Person per sq.km) City centre (km) (person per sq. km) 1.0 87012 9.0 4298 2.0 44934 10.0 3032 3.0 19866 11.0 2176 4.0 17632 12.0 1220 5.0 16733 13.0 920 6.0 12749 14.0 530 7.0 9772 15.0 230 8.0 9300 16.0 98

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Table 7: Distance-wise population density distribution in Karachi city, 1998. Distance from the city Population Distance from Population density Centre (km) density the city (Person per sq.km) (Person per Centre (km) sq.km) 1.0 33970 12.0 3012 2.0 22273 13.0 2560 3.0 18229 14.0 2216 4.0 8910 15.0 2134 5.0 8210 16.0 1415 6.0 7389 17.0 1093 7.0 7029 18.0 1032 8.0 6456 19.0 732 9.0 5551 20.0 523 10.0 4165 21.0 307 11.0 3592 22.0 183

Figure 3: A relation between population and area has been drawn that firmly evaluate the urban sprawling of Karachi city with the passage of time.

It is quite clear from the Tables 6 and 7 gradient which has more gentle slope in that the population density declined in 1998 as compared to 1981 (Fig. 3). 1998 as compared to 1981 up to 8 Kilometers and vice versa from 9 Sprawl measurement through fractal Kilometers. Therefore, we can say that the analysis population deconcentration of Karachi city The term “fractal geometry” was first continued with rapid space during the 17 introduced by Benoit Mandelbrot, based years period. In addition, from census data on a Latin noun “fractus”, derived from of (Table 6 and 7), during 17 the verb “frengere” which means “to years(1981−1998) population density, break” [21, 22]. Basically, it is the reduced to nearly three times this implies geometry that defines our universe and that the process of urban sprawl continues translates it into Mathematics. The word with a rapid pace. Its effect can be seen on “fractal” comes Unlike from Euclidean the graph of the population density geometry, fractal geometry has made

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possible to measure the fractional [ )) ) dimensions of irregular objects, and these ) ) objects are named as “fractals”. ) Theoretically, in the study of urban growth Where, and form by fractal geometry the smallest D: Fractal Dimension image forming units of a city figure can be N: Natural number; 0, 1, 2, 3…… considered as points so the topological C=N(s): Count of each “s” grid sizes dimension of city form is generally =s: grid size (e.g.: considered to be “0”. One study suggests ) Fractal Dimension (D) value of urban form The BCFD outputs a set of values for each ranges from 0 to 2 [21, 23, 24]. Fractal image of city, consisting box sizes(s), box dimension (FD) of an object may be counts (N(s)).the fractal values of urban measured by several methods, but the box space always fluctuate especially at counting method also known as BCFD minimum and maximum scales therefore algorithm is the most suitable for urban patterns need to b analyzed various measuring the FD of complex structures. times with different grid sizes to find the Additionally, it can be shown easily by fractal dimension of an urban space. visual presentation methods, i.e., city Therefore, we have computed multiple maps, and areal or satellite images. Peitgen measures of N(s) for different mesh sizes HO [20] calculated fractal dimension to to calculate the fractal dimension for analyze changes in spatial configuration as respective census data. follows:

Table 8: Fractal dimensions (D). Sr. No. Year Population Fractal Dimension (D) 1 1951 1,137,667 1.4019 2 1961 2,044,044 1.4397 3 1972 3,606,746 1.4922 4 1981 5,437,984 1.5501 5 1998 9,802,134 1.6898 6 2012 15,500,000 1.7026

Figure 4(a): Fractal dimension (D) growth of Karachi.

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Figure 4(b): Log (POP) as a linear function of D.

For the six time periods of Karachi, the land after the 1998 census. The best fit log-linear functions are population growth rate is higher than the displayed in Fig. 4. For only six growth rate of urbanized area from 1951 observations the R-Sq value is quite to 1998 but in 2012 it contradicts and high, log-linear function of population population growth rate (3.412) size over fractal dimensions shows decreases and growth rate of urbanized fairly good estimates. area (3. 648) increases. These results confirm the urban sprawl of Karachi The overall population density of (Table 5). Karachi increases for the census data of five time periods, but it decreases in The quick increase in fractal dimension 2012 (Fig. 4b). This shows that the between 1951 and 1998 reveals the population of Karachi has increased at rapid sprawling process due to informal rapid space during these time periods, settlement at periphery of the city. After and the increase in population is much 2000, the city was divided into 6 fast than its area but the decrease in districts this process is reflected in our population density in 2012 can be the calculation of relatively small change in cause of new established sub-centers between 1998 and 2012. fractal dimension between 1998 and 2012. While the central population density of city decreases with the passage of time An increase in the sprawl index value continuously (Fig. 4c) which shows the which exhibits the continuance of urban expansion of area and rapid increase in sprawl process after 1998 is observed, population in the vicinity of city. while a sustainability behavior of fractal dimension identifies that the urban form These estimations clearly show that the changes from concentrated to semi-linear rural land has been converted into urban forms.

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Figure 4(c): Overall population density of Karachi against fractal dimension.

Figure 4(d): Central population density versus fractal dimension.

CONCLUSION population density distribution and urban The study of urban sprawl has been a very form through fractal analysis also to key topic all over the world since last compute and characterize urban sprawl. decade. The complex patterns and forms of Urban expansion can easily be seen urban spatial development need both constantly, decreasing central population theoretical and methodological density and the developments towards the investigations which we have centralized. peripheral area as well. Due to this In this study, we have tried to present a peripheral expansion, in 2000 new district sprawl measurement methodology of the (Malir district) is established on North side sprawl dynamics through urban sprawl and in 2001 another district (Korangi index, population densities and fractal district) is established in South-East side analysis. These estimations have shown of the city. Due to the density increase in highly important conclusions related to various neighborhoods compact patterns urban sprawlness. In the case study of are also seen. Such urban development Karachi, we have attempted to measure pattern is subject to an increase in fractal urban sprawl using a sprawl index, further dimension. Meanwhile with the extension

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