星积分形曲面及其维数

基金项目: 国家杰出青年科学基金资助项目(59425003)

On Star Product Fractal Surfaces and Their Dimensions

1.
Institute of Rock Mechanics &hractals, China University of Mining and Technology, Beijing 100083, P. R. China;
2.
Department of Mathematics, Zhenjiang Teacher's College, Zhenjiang 212003, P. R. China;
3.
Department of hundamental Science, China University of Mining and Technology, Beijing 100083, P. R. China

摘要: 通过分形曲线定义了一类分形曲面(被称为星积分形曲面),讨论了这类分形曲面的分形维数,得出了分形曲线的维数与它们所构造出的分形曲面维数之间的关系。
- 维数 /
- 分形曲线 /
- 分形曲面 /
- 星积分形曲面
Abstract: In this paper, by using fractal curves, a family of fractal surfaces are defined. Each fractal surface of this family is called Star Product Fractal Surface (SPFS). A theorem of the dimensions of the SPFS is strictly proved. The relationship between the dimensions of the SPFS and the dimensions of the fractal curves constructing the SPFS is obtained.
- dimension /
- fractal curve /
- fractal surface /
- SPFS

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