| 一类Weierstrass型函数图像的Box维数 |
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| 引用本文： | 张静,刘鸿博.一类Weierstrass型函数图像的Box维数[J].四川轻化工学院学报,2013(5):74-76. |
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| 作者姓名： | 张静 刘鸿博 |
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| 作者单位： | 四川水利职业技术学院,成都611830 |
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| 摘 要： | Weierstrass函数是一类处处不可微的函数，其函数图像具有分形性质。研究Weierstrass函数图像的分形维数在分形几何中具有非常重要的地位。通过研究一类Weierstrass型函数W（x）=∑^∞k=1 αkφti（bkx＋θk）的图像的Box维数，证明了这类函数图像的Box维数为2＋lim n→∞（logan／logbn），从而进一步揭示出这类Weierstrass函数图像的Hausdorff维数与Box维数之间的关系。
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| 关 键 词： | Weierstrass型函数 函数图像 Box维数 |
Box Dimension of a Class of Weierstrass Function |
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| ZHANG Jing,LIU Hong-bo.Box Dimension of a Class of Weierstrass Function[J].Journal of Sichuan Institute of Light Industry and Chemical Technology,2013(5):74-76. |
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| Authors: | ZHANG Jing LIU Hong-bo |
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| Affiliation: | (Sichuan Water Conservancy Vocational College, Chengdu 611830, China) |
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| Abstract: | Weierstrass function is everywhere continuous and nowhere differentiable. Its graph has fractal properties. Studying the fractal dimension of Weierstrass function graph plays an important role in fractal geometry. The Box-dimension of graph of a kind of Weierstrass-type function is studied. It is proved that its Box-dimension is equal to 2＋lim n→∞（logan/logbn）,and the relationship between Hausdorff dimension and Box dimension is progressively revealed. |
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| Keywords: | Weierstrass function graph Box dimension |
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