Measuring the Urban Space-filling Efficiency using Fractal Dimension: The Case of Safranbolu, Turkey

K. Mert CUBUKCU, Ph.D.

Assistant Professor

Dokuz Eylul University, Turkey

mert.cubukcu@deu.edu.tr

Ebru CUBUKCU, Ph.D.

Assistant Professor

Dokuz Eylul University, Turkey

ebru.cubukcu@deu.edu.tr

Abstract Fractals are spatial entities that are irregular in terms of geometry and independent

from scale. Recent research has demonstrated that the urban form can not be fully

described by Euclidean geometry, but rather be treated as fractals (Batty and Longley,

1987; Benguigui and Daoud, 1991; Batty and Xie, 1996; 1999; Shen 1997; 2002).

Fractal dimension is a quantitative measure of the efficiency of space-filling. It is

almost always not a whole number, which implies that fractal objects occupy

irregularly shaped spaces (Ball, 2004).

Sustainability, by definition, requires the usage of resources in their most efficient

form. Sustainability development should ensure that human economic systems last

longer and have less impact on ecological systems. Undoubtedly, this can only be

achieved through an efficiently organized urban form and efficient space-filling. The

efficiency of urban form can well be measured using fractal dimensions of the built-

up urban areas. As the city grows, its fractal dimension is expected to increase as the

city becomes increasingly dense, using the three dimensional space more efficiently

(Ball, 2004). Batty and Longley, for example, shows that the fractal dimension of

London has increased from 1.32 to 1.79 between the years 1820 and 1962, indicating

a better form of spatial organization and more efficient space-filling. This paper

examines the urban space-filling efficiency of a historic city, Safranbolu, using its

fractal dimensions to investigate in which time period the urban form had the most

efficient form of spatial organization. Time series spatial data pertaining the years

between 1960 and 2007 are utilized.

Safranbolu is one of the 138 historic cities listed in UNESCOs World Heritage List,

and it is one of the two listed cities in Turkey, the other being Istanbul. Safranbolu

was added to list in 1994 due to its well-preserved Ottoman era architecture and urban

pattern. Safranbolu's architecture and urban pattern influenced the urban development

throughout much of the Ottoman Empire. Safranbolu is thus thoroughly a good

representative of Ottoman urban pattern in the 18th and 19th centuries. The city of

Safranbolu, outside the historic core, is also a good representative of the planned post-

imperial Republican era.

In spatial analysis, fractal dimensions are mainly computed using the box-counting

method and the mass-radius method (Shen, 2002). Batty and Longley (1994) and

Shen (1997) apply the box-counting method and Batty and Longley (1987),

Benguigui and Daoud (1991), and Batty and Xie (1996) apply the mass-radius

method. A systematic analysis of planar urban fractal dimensions of Safranbolu is

derived for 5 different time periods using the Box-Counting Fractal Dimension

algorithm described in detail in Shen (1997). The approximation procedure in

algorithm is based on the work of Mandelbrot (1983):

n(s) * sd = U,

where n(s) is the number of boxes containing the built-up urban areas U, d is the true

fractal dimension. The estimated fractal dimension D of the true fractal dimension d is

derived by estimated slope of the log(n(s)) and log(1/s) graph (Shen, 2007). That is to

say, the fractal dimension values for the 5 different time periods of the urban form of

Safranbolu are the least-square estimates of their true fractal dimensions:

log(n(s)) = log(U) + DLog(1/s) + s,

where log(U) is the constant with U being the built-up urban area size, s is the error term, and D is the estimated fractal dimension.

The data used in the study were derived from the digital and hardcopy aerial

photographs available from the Municipality of Safranbolu. The photographs were

first refined using image processor software, Photohop version 6, and then scaled,

registered, and vectorized using GIS software, ArcGIS 9. The fractal dimensions are

then calculated for each time period using fractal analysis software, Fractalyse.

The results are parallel to the claims in the literature. The city of Safranbolu has

moved from a less efficient spatial organization and space-filling to a more efficient

one between the years 1960 and 2007. This achievement towards a more sustainable

type of urban form is an expected result of population increase and increased density

through modern planning efforts.

References Ball, P., 2004, Critical Mass: How One Thing Leads to Another, Arrow Books,

London.

Batty, M., and Longley, P. A., 1987, Urban shapes as fractals. Area, 19, 215221.

Batty, M., and Xie, Y., 1996, Preliminary evidence for a theory of the fractal city.

Environment and Planning A, 28, 17451762.

Batty, M., and Xie, Y., 1999, Self-organized criticality and urban development.

Discrete Dynamics in Nature and Society, 3, 109124.

Benguigui, L., and Daoud, M., 1991, Is the suburban railway system a fractal?

Geographical Analysis, 23, 362368.

Mandelbrot, B., 1983, The Fractal Geometry of Nature, W. H. Freeman, San

Francisco.

Shen, G., 1997, A fractal dimension analysis of urban transportation networks.

Geographical & Environmental Modelling, 1, 221236.

Shen, G., 2002, Fractal dimension and fractal growth of urbanized areas, International

Journal of Geographical Information Science, 16(5), 419-437