ABSTRACT Urban growth prediction has acquired an important consideration in urban sustainability. An effective approach of urban prediction can be a valuable tool in urban decision making and planning. A large urban development has been occurred during last decade in the touristic village of Pogonia Etoloakarnanias, Greece, where an urban growth of 57.5% has been recorded from 2003 to 2011. The prediction of new urban settlements was achieved using fractals and theory of chaos. More specifically, it was found that the urban growth is taken place within a Sierpinski carpet. Several shapes of Sierpinski carpets were tested in order to find the most appropriate, which produced an accuracy percentage of 70.6% for training set and 81.8% for validation set. This prediction method can be effectively applied in urban growth modelling, once cities are fractals and urban complexity can be successfully described through a Sierpinski tessellation.
Cite this paper
D. Triantakonstantis, "Urban Growth Prediction Modelling Using Fractals and Theory of Chaos," Open Journal of Civil Engineering, Vol. 2 No. 2, 2012, pp. 81-86. doi: 10.4236/ojce.2012.22013.
 J. I. Barredo, M. Kasanko, N. McCormick and C. Lavalle, “Modelling Dynamic Spatial Processes: Simulation of Urban Future Scenarios through Cellular Automata,” Landscape and Urban Planning, Vol. 64, No. 3, 2003, pp. 145-160. doi:10.1016/S0169-2046(02)00218-9
 M. Batty and P. A. Longley, “Fractal Cities: A Geometry of Form and Function,” Academic Press, London, 1994.
 B. B. Mandelbrot, “The Fractal Geometry of Nature,” W. H. Freeman and Company, New York, 1983.
 B. T. Milne, “The Utility of Fractal Geometry in Landscape Design,” Landscape and Urban Planning, Vol. 21, No. 1-2, 1991, pp. 81-90.
 I. Thomas, P. Frankhauser and C. Biernacki, “The Morphology of Built-Up Landscapes in Wallonia (Belgium): A Classification Using Fractal Indices,” Landscape and Urban Planning, Vol. 84, No. 2, 2008, pp. 99-115.
 C. Tannier, I. Thomas, G. Vuidel and P. Frankhauser, “A Fractal Approach to Identifying Urban Boundaries,” Geographical Analysis, Vol. 43, No. 2, 2011, pp. 211- 227. doi:10.1111/j.1538-4632.2011.00814.x
 P. M. Allen, “Cities and Regions as Self-Organizing Systems: Models of Complexity,” Gordon and Breach, New York, 1997.
 M. Batty, “New Ways of Looking at Cities,” Nature, Vol. 377, No. 6550, 1995, p. 574. doi:10.1038/377574a0
 F. Wu, “An Experiment on the Generic Polycentricity of Urban Growth in a Cellular Automatic City,” Environment and Planning B: Planning and Design, Vol. 25, No. 5, 1998, pp. 731-752. doi:10.1068/b250731
 S. Berling-Wolff and J. Wu, “Modeling Urban Landscape Dynamics: A Case Study in Phoenix, USA,” Urban Ecosystems, Vol. 7, No. 3, 2004, pp. 215-240.
 L. Poelmans and V. A. Rompaey, “Complexity and Performance of Urban Expansion Models,” Computers, Environment and Urban Systems, Vol. 34, No. 1, 2010, pp. 17-27. doi:10.1016/j.compenvurbsys.2009.06.001
 M. Batty and P. A. Longley, “The Morphology of Urban Land Use,” Environment and Planning B: Planning and Design, Vol. 15, No. 4, 1988, pp. 461-488.
 Y. Chen and S. Jiang, “An Analytical Process of the Spatio-Temporal Evolution of Urban Systems Based on Allometric and Fractal Ideas,” Chaos, Solitions & Fractals, Vol. 39, No. 1, 2009, pp. 49-64.
 Y. Chen and J. Lin, “Modeling the Self-Affine Structure and Optimization Conditions of City Systems Using the Idea from Fractals,” Chaos, Solitions & Fractals, Vol. 41, No. 2, 2009, pp. 615-629.
 M. J. Bechmann, “City Hierarchies and Distribution of City Sizes,” Economic Development and Cultural Change, Vol. 6, No. 3, 1958, pp. 243-248. doi:10.1086/449769
 M. Herold, H. Couclelis and K. C. Clarke, “The Role of Spatial Metrics in the Analysis and Modeling of Urban Land Use Change,” Computers, Environment and Urban Systems, Vol. 29, No. 4, 2005, pp. 369-399.
 K. C. Seto and M. Fragkias, “Quantifying Spatiotemporal Patterns of Urban Land Use Change in Four Cities of China with Time Series Landscape Metrics,” Landscape Ecology, Vol. 20, No. 7, 2005, pp. 871-888.
 M. Herold, J. Scepan and K. C. Clarke, “The Use of Remote Sensing and Landscape Metrics to Describe Structures and Changes in Urban Land Uses,” Environment and Planning A, Vol. 34, No. 8, 2002, pp. 1443-1458.
 Self-Reference Is Omitted to Facilitate the Blind Review.
 P. Frankhauser, “Comparing the Morphology of Urban Patterns in Europe—A Fractal Approach,” In: A. Borsdorf and P. Zambri, Ed., European Cities—Insights and Outskirts, Report COST Action 10 Urban Civil Engineering, Structures, Brussels, Vol. 2, 2004, pp. 79-105.