由几何反演导出的分形几何
Fractal Geometry Derived from Geometric Inversion
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摘要: 本文介绍了由几何反演而导出的自反分形概念.构造了一个对称的,分叉自反分形曲线和一个自反分形尘集.推广了分形密切的概念而且提出了一个新的概念——分形包络.最后给出了“肥皂”和“鸡蛋”的两个自反分形的实例.Abstract: In this paper, the conception of fractal geometry derived from geometric inversion is introduced.A ramified self-inverse fractal with symmetry and a self-inverse fractal dust set are constructed.The authors extend the conception of the fractal osculation and propose a new notion——fractal envelope.Finally, two examples of self-inverse fractal (soap and egg) are given.
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Key words:
- geometric inversion /
- self-inverse fractal /
- fractal osculation /
- fractal envelope
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[1] Mandelbrot,B.B.,Fractals Forms,Chance and Dimension,Freeman,San Francise(1977). [2] Mandelbrot,B.B.,The Fractals Geometry of Nature,Freeman and Company(1983). [3] 谢和平、陈至达,分形几何及其在断口分析中的应用,MMMⅠ文集(1987). [4] 谢和平、张永平,分形几何与自然界中的分形几何律,江苏省数学年会((1988,9). [5] Underwood,Eruine and Kingshuk Banerji,Invine review fractals in fractography,Materials Science and Engineering,80(1986). [6] Gilbert,W.J.,Fractal geometry derived from complex bases,Math.Int.,4,2(1982). [7] 谢和平、陈至达,分形几何与岩石断裂,力学学报,20, 3 (1988),264. -
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