周长-面积关系及分形维数的计算机模拟

The Computer Simulation of Fractal Dimension-Ality with Perimeter-Area Relation

1.
Institute of Metal Research, Academia Sinica, Shenyang 110015, China;
2.
International Center for Materials Physics, Academia Sinica, Shenyang 110015, China

摘要: 本文利用分形理论中周长-面积关系的基本概念，对初始形状为三角形的不同大小的Koch曲线围成的岛，模拟了不同条件下，测量D值的变化规律，并进一步指出应用这一关系所应满足的条件及实际测量中有限层次的影响，探讨了所需条件在实际应用中的物理意义。
- 分形维数 /
- 初始长度 /
- 层次 /
- 码尺
Abstract: The paper makes use of perimeter-area relation to simulate the low of variation of fractal dimensionality D under different conditions at the islands closed by Koch curve with initial shapes of equilateral triangles. The conditions necessarily to be met in measurement and the influence of limited level are indicated with application of perimeter-area relation. The physical meaning of these conditions is discussed on realistic application.
- Fractal dimensionality /
- initial length /
- level /
- yardstick