Fractal Analysis of Area-Perimeter Relationship of Some Selected Countries of the World
Keywords:
Fractal dimension, Area- Perimeter relation, box counting, self similarity.
Abstract
Boundaries of six selected countries one from each continent were studied, using fractal dimension technique. The Area – Perimeter relation method was used, where land area covered and boundary length of designated countries were measured in the unit of known box size (Box counting). The log-log plots of these variables were obtained and the slopes were measured as the required dimensions. Fractal dimensions determined lie between 1.19 and 1.55. The scale size of the maps, and the number of states both had no significant effect (p>0.05) on the fractal dimensions obtained.
References
Alabi, B. 2001. “From Vibrations to Fractals: Excitement at the Frontiers of Knowledge”. An Inaugural Lecture Presented. University of Ibadan.
Graf, J.C. 1991. “The importance of resolution limits to the interpretation of Fractal descriptions of fine particles”. Powder Technol., 67, 83-85.
Jain, P.S. 1986. “Fractal dimensions of clouds around Madras” Mausam, 40, 311-316.
Klonowski, W. 2000. ”Signal and Image Analysis Using Chaos Theory and Fractal Geometry” http://www.fractal.org/Life-Science-Technology/publications/ Fractal signals.
Mandelbrot, B.B. 1977. “Fractals Form, Chance, and Dimensions”. W.H. Freeman, San Francisco.
Milne, B.T. 1991. “The utility of fractal geometry in landscape design” Lands. Urb. planng, 21, 81-90.
Morrison, A.I., Srokosz M.A. 1993. “Estimating the fractal dimension of the sea surface: a first attempt “ann. Geophysics, 11, 648-658.
Munro, B.H. 2001. Statistical methods for health care research, fourth edition, Lippincott, 2001, pp 123-133.
Nagai, T., Yano, Y. 1990. “Fractal structure of deformed potato starch and its sorption characteristics”. Journal of food science, 55, 1334-1337.
Ogata, Y., Katsura, K. 1991. “Maximum likelihood estimates of the fractal dimension for random spatial patterns”. Biometrika, 78 (3), 463-474.
Peleg, M. , Normand, M.D. 1985. “Characterization of the ruggedness of instant Coffee particle shape by natural fractals” Journal of food science, 50, 829-831
Smith Jr., T.G., Marks, W.B., Lange G.D., Sheriff Jr.,W.H., Neale, E.A. 1989. “A fractal analysis of cell images” Journal of Neuroscience. 27, 173-180.
Smith Jr., T.G., Lange G.D., Marks W.B. 1996. “Fractal methods and result in cellular morphology-dimensions, lacunarity and multifractals” Journal of Neuroscience, 69, 123-136.
Takayasu, H. 1990. “Fractals in the physical sciences” Manchester University press, Manchester.
Thomas, T.R., Thomas, A.P. 1988. “Fractals and engineering surface roughness” Surface Topography, 1, 143-152.
Yano, T., Nagai, T. 1989. “Fractal structure of starchy materials transformed with hydrophilic alcohols” Journal of Food Engineering, 10, 123-133.
Graf, J.C. 1991. “The importance of resolution limits to the interpretation of Fractal descriptions of fine particles”. Powder Technol., 67, 83-85.
Jain, P.S. 1986. “Fractal dimensions of clouds around Madras” Mausam, 40, 311-316.
Klonowski, W. 2000. ”Signal and Image Analysis Using Chaos Theory and Fractal Geometry” http://www.fractal.org/Life-Science-Technology/publications/ Fractal signals.
Mandelbrot, B.B. 1977. “Fractals Form, Chance, and Dimensions”. W.H. Freeman, San Francisco.
Milne, B.T. 1991. “The utility of fractal geometry in landscape design” Lands. Urb. planng, 21, 81-90.
Morrison, A.I., Srokosz M.A. 1993. “Estimating the fractal dimension of the sea surface: a first attempt “ann. Geophysics, 11, 648-658.
Munro, B.H. 2001. Statistical methods for health care research, fourth edition, Lippincott, 2001, pp 123-133.
Nagai, T., Yano, Y. 1990. “Fractal structure of deformed potato starch and its sorption characteristics”. Journal of food science, 55, 1334-1337.
Ogata, Y., Katsura, K. 1991. “Maximum likelihood estimates of the fractal dimension for random spatial patterns”. Biometrika, 78 (3), 463-474.
Peleg, M. , Normand, M.D. 1985. “Characterization of the ruggedness of instant Coffee particle shape by natural fractals” Journal of food science, 50, 829-831
Smith Jr., T.G., Marks, W.B., Lange G.D., Sheriff Jr.,W.H., Neale, E.A. 1989. “A fractal analysis of cell images” Journal of Neuroscience. 27, 173-180.
Smith Jr., T.G., Lange G.D., Marks W.B. 1996. “Fractal methods and result in cellular morphology-dimensions, lacunarity and multifractals” Journal of Neuroscience, 69, 123-136.
Takayasu, H. 1990. “Fractals in the physical sciences” Manchester University press, Manchester.
Thomas, T.R., Thomas, A.P. 1988. “Fractals and engineering surface roughness” Surface Topography, 1, 143-152.
Yano, T., Nagai, T. 1989. “Fractal structure of starchy materials transformed with hydrophilic alcohols” Journal of Food Engineering, 10, 123-133.
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