Fractals and the accuracy of geographical measures
- Michael F. Goodchild
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The problems of estimating line length, area, and point characteristics in the earth sciences have generated substantial but independent literatures. All three problems are of increasing concern given the current interest in digital capture, processing, and the storage of geographically referenced data. In the case of qualitative maps, all three are shown to be related to Mandelbrot's fractional dimension D (Mandelbrot, 1977) which allows the dependence of each on sampling density to be predicted. The general results are confirmed by simulation on surfaces of constant D. They also imply that certain improvements can be made in a number of previously proposed methods.
- Beckett, P., 1977, Cartographic generalization: Cartographic J., v. 14, p. 49–50.
- Frolov, Y. S. and Maling, D. H., 1969, The accuracy of area measurements by point counting techniques: Cartographic J., v. 6, p. 21–35.
- Goodchild, M. F. and Moy, W. S., 1977, Estimation from grid data: the map as a stochastic process,in Proceedings of the Commission on Geographical Data Sensing and Processing, Moscow, 1976, (R. F. Tomlinson, ed.), Ottawa: International Geographical Union, Commission on Geographical Data Sensing and Processing.
- Håkanson, L., 1978, The length of closed geomorphic lines: Mathematical Geol. v. 10, p. 141–167.
- Lloyd, P. R., 1976, Quantization error in area measurement: Cartographic J. v. 13, p. 22–26.
- Mandelbrot, B. B., 1967, How long is the coast of Britain? Statistical self-similarity and fractional dimension: Science v. 156, p. 636–638.
- Mandelbrot, B. B., 1975a, Stochastic models of the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands: Proceedings of the National Academy of Sciences, v. 72, p. 3825–3828.
- Mandelbrot, B. B., 1975b, On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars: J. Fluid Mechanics v. 72, p. 401–416.
- Mandelbrot, B. B., 1977, Fractals: Form, Chance and Dimension: Freeman, San Francisco, 365 p.
- Maling, D. M., 1968, How long is a piece of string?: Cartographic J. v. 5, p. 147–156.
- Matheron, G., 1967, Éléments pour une Théorie des Mileux Poreux: Masson, Paris, 166 p.
- Moy, W. S., 1977, Estimation from grid data: the map as a stochastic process. Unpublished M.A. Dissertation, Department of Geography, University of Western Ontario.
- Muller, J. C., 1978, Map gridding and cartographic errors: a recurrent argument: Canadian Cartographer v. 14, p. 152–167.
- Orey, S., 1970, Gaussian sample functions and the Hausdorff dimension of level crossings. Zeitschrift fur Wahrscheinlichkeitstheorie und verwandte Gebiete v. 15, p. 249–256.
- Richardson, L. F., 1961, The problem of contiguity: General Systems Yearbook v. 6, p. 139–187.
- Scheidegger, A. E., 1970, Theoretical geomorphology (2nd ed.): Springer Verlag, New York, 333 p.
- Switzer, P., 1975, Estimation of the accuracy of qualitative maps,in Display and analysis of spatial data, (J. C. Davis and M. J. McCullagh, eds.): Wiley, London, 378 p.
- Tobler, W. R., 1974, The accuracy of categorical maps: Department of Geography, University of Michigan, Cartographic Laboratory Report Number 4.
- Tomlinson, R. F., Calkins, H. W. and Marble, D. F., 1976,Computer Handling of Geographical Data UNESCO Press, Paris, 214 p.
- Fractals and the accuracy of geographical measures
Journal of the International Association for Mathematical Geology
Volume 12, Issue 2 , pp 85-98
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- Kluwer Academic Publishers-Plenum Publishers
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- spatial distributions
- map analysis
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- Author Affiliations
- 1. Department of Geography, The University of Western Ontario, N6A 5C2, London, Ontario, Canada