| 按严格递归法则生成的多重分形及其谱维数方程 |
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| 引用本文： | 李军.按严格递归法则生成的多重分形及其谱维数方程[J].上海师范大学学报(自然科学版),1994(2). |
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| 作者姓名： | 李军 |
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| 摘 要： | 本文在给出了广义Ｈａｕｓｄｏｒｆｆ维数定义的基础上得到了按严格递归法则生成的多重分形的谱维数Ｄｑ＝Ｄ（ｑ）的一般函数关系式─谱维数方程．作为谱维数方程的应用，得到了一维Ｃａｎｔｏｒ集的Ｄｑ谱和ｆ（ａ）谱的解析表达式
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| 关 键 词： | 多重分形 广义Hausdorff维数，分形测度 f（a）谱 |
Multifractals Created by Exact Recursive Rule and the Equation of Dimension's Spectrum |
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| Li Jun.Multifractals Created by Exact Recursive Rule and the Equation of Dimension''''s Spectrum[J].Journal of Shanghai Normal University(Natural Sciences),1994(2). |
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| Authors: | Li Jun |
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| Institution: | Department of Physics |
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| Abstract: | Hausdorff Dimension is an improtant tool of studying simple fractals. In theis paper we have generalized Hausdorff Dimension in order to discuss multifractals and obtain a general equation about the spectrum dimension Dg of multifractals created by exact recursive rule. This general equation is derived by the definition of Generalized Hausdorff Dimensions. As a model we use a simple one-dimensional Cantor set whose Dg and f (a) spectrum can be found analytically. |
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| Keywords: | multifractals Generalized Hausdorff dimensions fractal measure the f(a) spectrum |
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