| 分形集的模拟与维数计算 |
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| 引用本文： | 覃凤清.分形集的模拟与维数计算[J].宜宾学院学报,2007,7(6):7-9. |
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| 作者姓名： | 覃凤清 |
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| 作者单位： | 宜宾学院,计科系,四川,宜宾,644000 |
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| 摘 要： | 分形维数的定义突破了拓扑学中集合维数都是整数的局限,从整数维到分数维,是数学理论的重大变革与发展.文章在研究分形维数基本理论的基础上,采用递归算法,通过计算机编程,对几个分形集进行了模拟,计算出其相应的分形维数.从实验可以看出,这些分形集具有某种自相似的形式,一般分形集的分形维数严格大于其相应的拓扑维数.
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| 关 键 词： | 分形维数 拓扑维数 分形集 自相似 |
| 文章编号： | 1671-5365（2007）06-0007-03 |
| 修稿时间： | 2007-04-03 |
Simulation and Dimension Calculation of Fractal Set |
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| Authors: | QIN Feng-qing |
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| Institution: | Department of Computer, Yibin University, Yibin 644007, China |
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| Abstract: | The definition of fractal dimension from integer to fraction breaks through the limitation of topology in which the dimension is integer;it is the important change and development of mathematical theory.Based on the fundamentals on fractal dimension,adopting recursion algorithm,through computer programming,several fractal concourses are simulated,and their corresponding dimensions are calculated.From the experimental results,we can find that these fractal set have somewhat self-similar forms,and that the fractal dimension of common fractal concourse is strictly greater than its corresponding topological dimension. |
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| Keywords: | Fractal Dimension Topological Dimension Fractal Set Self-Similarity |
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