Abstract
Richardson analysis, one of the principal methods of fractal analysis, is performed by measuring the perimeter of a curve with strides of varying length and constructing a log-log plot of perimeter against stride length. Certain simple geometrical forms can produce linear plots that mimic fractal behavior, and two smooth curves have been discovered that produce linear Richardson plots for strides varying by two orders of magnitude or more. The existence of such curves was not suspected before this study. Richardson analyses that suggest fractal geometry of low dimension or over a limited range of stride length should be checked against the source data for independent evidence of self-similarity.
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References
Anonymous, 1970, National Atlas of the United States of America: United States Department of the Interior and United States Geological survey, 417 p.
Artyukhin, Yu. V., 1987, Geneziz i Dinamika kos “Azovskogo” Tipa (Genesis and Dynamics of “Azov”-Type Spits): Geomorfologiya, v. 3, p. 27–30.
Aviles, C. A., and Scholz, C. H., 1987, Fractal Analysis Applied to Characteristic Segments of the San Andreas Fault: J. Geophys. Res., v. 92, n. B1, p. 331–344.
Carr, J. R., and Warriner, J. B., 1989, Relationship Between the Fractal Dimension and Joint Roughness Coefficient: Bull. Am. Assoc. Eng. Geologists, v. 26, p. 253–263.
Cullin, W. E. H., 1988, Dimension and Entropy in the Soil-covered Landscape: Earth Surf. Proc. Landforms, v. 13, p. 619–648.
Cullin, W. E. H., and Datko, M., 1987, The Fractal Geometry of the Soil-Covered Landscape: Earth Surf. Proc. Landforms, v. 12, p. 369–385.
Davis, W. M., 1896, The Outline of Cape Cod: Proceedings of the American Academy of Arts and Sciences, v. 31, p. 303–332.
Evans, O. F., 1942, The Origins of Spits, Bars, and Related Structures: J. Geol., v. 50, p. 846–865.
Fairbridge, R. W., 1968, Encyclopedia of Geomorphology: Reinhold, New York, 1295 p.
Johnson, D. W., 1919, Shore Processes and Shoreline Development: Hafner, New York, 584 p.
Komar, P. D., 1976, Beach Processes and Sedimentation: Prentice Hall, Englewood Cliffs, NJ, 430 p.
Langbein, W. B., 1963, The Hydraulic Geometry of a Small Tidal Estuary: Bull. Int. Assoc. Scientific Hydrol., v. 8, p. 84–94.
Lawrence, J. D., 1972, A Catalog of Special Plane Curves: Dover, New York, 218 p.
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., 1983, The Fractal Geometry of Nature: Freeman, San Francisco, 468 p.
Pethick, J., 1984, An Introduction to Coastal Geomorphology: E. Arnold, London, 260 p.
Richardson, L. F., 1961, The Problem of Contiguity,in A. Rapaport, L. von Bertalanfy, and R. Meier (Eds.), General Systems: Yearbook for the Society for General Systems Research, v. 6, p. 139–187.
Schumm, S. A., 1956, Evolution of Drainage Basins and Slopes in Badlands at Perth Amboy, New Jersey: Geological Soc. Am. Bull., v. 67, p. 597–646.
Yasso, W. E., 1965, Plan Geometry of Headland Bay Beaches: Coastal Res. Notes, v. 11, p. 8–9.
Zenkovich, P. V., 1967, Processes of Coastal Development: Oliver and Boyd, London, 738 p.
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Dutch, S.I. Linear Richardson plots from non-fractal data sets. Math Geol 25, 737–751 (1993). https://doi.org/10.1007/BF00893176
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DOI: https://doi.org/10.1007/BF00893176