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And simulation: in Digital Image Processing in Remote Sensing, J.P. Muler, (Ed.): Taylor & Francis, pp. 177–212. Google Scholar Lovejoy, S., Schertzer, D., and Ladoy, P., 1986, Fractal characterisation of inhomogeneous geophysical measuring networks: Nature (London) 319, 43–44.Article Google Scholar Lovejoy, S., Schertzer, D. and Tsonis, A.A., 1987, Functional box-counting and multiple elliptical dimensions in rain: Science 235, 1036–1038.Article Google Scholar Mandelbrot, B.B., 1967, How long is the coast of Britain? Statistical self-similarity and fractional dimension: Science 156, 636–638.Article Google Scholar Mandelbrot, B.B., 1975, Stochastic models for the Earth’s relief, the shape and the fractal dimension of coastlines, and the number-area rule for islands: Proc. Nal. Acad. Sci. U.S.A. 72, 3825–3828.Article Google Scholar Mandelbrot, B.B., 1977, Fractals: Form, Chance and Dimension: Freeman, San Francisco. Google Scholar Mandelbrot, B.B., 1982. The Fractal Geometry of Nature: Freeman, San Francisco. Google Scholar Mandelbrot, B.B., 1984, Fractals in physics: Squig clusters, diffusions, fractal measures, and the uni-city of fractal dimensionality: J. Stat. Phys. 34, 895–929.Article Google Scholar Mark, D.M., 1975, Geomorphometric parameters: A review and evaluation: Geograf. Ann. Ser. A 3, 165–177.Article Google Scholar Mark, D.M., and Aronson, P.B., 1984, Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology: Math. Geol. 16, 671–683.Article Google Scholar Morse, D.R., Lawton, J.H., Dodson, M.M., and Williamson, M.H., 1985, Fractal dimension of vegetation and the distribution of arthropod body lengths: Nature (London) 314, 731–733.Article Google Scholar Muller, J.-C., 1986, Fractal dimension and inconsistencies in cartographic line representations: Cartog. J. 23, 123–130. Google Scholar Pentland, A.P., 1984, Fractal-based description of natural scenes: IFFE PAMI 6, 661–674.Article Google Scholar Peitgen, H.-O., and Saupe, D., Eds., 1988, The Science of Fractal Images: Springer-Verlag, Berlin. Google Scholar Richardson, L.F., 1961, The problem of contiguity: An appendix to ‘Statistics of deadly quarrels’: General Sys. Yearbook 6, 139–187. Google Scholar Roy, A., Gravel, G., and Gauthier, C., 1987, Measuring the dimension of surfaces: A review and appraisal of different methods: Proc. Auto-Carto Eight, 68–77. Google Scholar Scholz, C.H., and Aviles, C.A., 1986, The fractal geometry of faults and faulting: Earthquake Source Mechanics (Geophysical Monograph 37), M. Ewing Ser. 6. Google

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Presented at MGUS-87, Redwood City, CA. Google Scholar Goodchild, M.F., 1980, Fractals and the accuracy of geographical measures: Math. Geol. 12, 85–98.Article Google Scholar Goodchild, M.F., 1982, The fractional Brownian process as a terrain simulation model: Model. Simulation 13, 1133–1137. Google Scholar Goodchild, M.F., and Mark, D.M., 1987, The fractal nature of geographic phenomena: Ann. AAG 77, 265–278. Google Scholar Goodchild, M.F., Klinkenberg, B., Glieca, M., and Hasan, M., 1985, Statistics of hydrologic networks on fractional Brownian surfaces: Model. Simulation 16, 317–323. Google Scholar Hakanson, L., 1978, The length of closed geomorphic lines: Math. Geol. 10, 141–167.Article Google Scholar Hobson, R.D., 1972, Surface roughness in topography: A quantitative approach: in Spatial Analysis in Geomorphology, R.J. Chorley, (Ed.): Methuen, London, pp. 221–245. Google Scholar Hunt, C.B., 1967, Physiography of the United States: Freeman, San Francisco. Google Scholar Kagan, Y.Y., and Knopoff, L., 1980, Spatial distribution of earthquakes: The two-point correlation function: Geophys. J. R. Astron. Soc. 62, 303–320. Google Scholar Kadanoff, L.P., 1986, Fractals, where’s the physics?: Phys. Today, February, 1986. Google Scholar Kennedy, S.K., and Lin, W.-H., 1986, Fract-A fortran subroutine to calculate the variables necessary to determine the fractal dimension of closed forms: Comput. Geosci. 12, 705–712.Article Google Scholar Kent, C., and Wong, J., 1982, An index of littoral zone complexity and its measurement: Can. J. Fish Aquatic Sci. 39, 847–853.Article Google Scholar Klinkenberg, B., 1988, Tests of a fractal model of topography: Ph.D. thesis, University of Western Ontario. Google Scholar Lovejoy, S., 1982, Area-perimeter relation for rain and cloud areas: Science 216, 185–187.Article Google Scholar Lovejoy, S., and Mandelbrot, B.B., 1985, Fractal properties of rain, and a fractal model: Tellus 37 (A), 209–232. Google Scholar Lovejoy, S., and Schertzer, D., 1985, Generalized scale invariance in the atmosphere and fractal models of rain: Water Resources Res. 21(8), 1233–1250.Article Google Scholar Lovejoy, S., and Schertzer, D., 1986, Scale invariance, symmetries, fractals, and stochastic simulations of atmospheric phenomena: Bull. Am. Meteorol. Soc. 67, 21–32.2.0.CO;2" data-track-item_id="10.1175/1520-0477(1986)0672.0.CO;2" data-track-action="Article reference" data-track-value="Article reference" href=" aria-label="Article reference 32" data-doi="10.1175/1520-0477(1986)0672.0.CO;2">Article Google Scholar Lovejoy, S., and Schertzer, D., 1988, Extreme variability, scaling and fractals in remote sensing: analysis