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摘要: 本文讨论分形图形周界和面积的关系;指出:在现实存在的有限层次自相似结构的近似分形图形中,Mandelbrot的周界-面积分维关系不适用。这可能是一些用此方法测出的分维值随码尺大小变化的根本原因。Abstract: The relationship of perimeter with area (P/A relation) of fractal island is discussed. It is shown that Mandelbrot's fractal relation between Koch perimeter and area does not hold in the island with finite self-similar generations. This might be the reason why the fractal dimension measured with P/A relation varied with the length of yardstick in previous work.
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Key words:
- fractal /
- fractal dimension /
- Koch island /
- self-similarity
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Mandelbrot B B. The Fractal Geometry of Nature. New York: Freeman, 1983: 459. Mandelbrot B B, Passoja D E, Paullay A J. Nature, 1984, 308: 721. Feder J. Fractals. New York: Plenum, 1987: 200. Pande C S, Richards L E, Louat N, et al. Acta Metall, 1987, 35: 1633. 谢和平, 陈至达. 力学学报, 1988, 20: 264. Mu Z Q, Lung C W. J Physics D, 1988, 21: 848. Wang Z G, Chen D L, Jiang X X, et al. Scripta Metall, 1988, 22: 827. Zhou X Y, Chen D L, Ke W, et al. Materials Letters, 1989, 12: 473. Zhang S Z, Lung C W. J Phys D, 1989, 22: 790. Lung C W, Zhang S Z. Physica D, 1989, 38: 242. Lung C W, Mu Z O. Phys Rev B, 1988, 38: 11781. 龙起易, 穆在勤, 等. 待发表.
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