随机Koch曲线岛及其分维测定的计算机模拟  

Computer Modeling on Both Random Koch Curve Islands and Determination for Their Fractal Dimension

作　　者：李玉清[1,2,3] 李蓬[1,2,3] 赵咏秋 刘雅晶[1,2,3] 李启楷[1,2,3] 

机构地区：[1]大冶特殊钢股份有限公司技术中心 [2]北京航空航天大学 [3]北京科技大学

出　　处：《中国图象图形学报（A辑）》1998年第3期205-211,共7页Journal of Image and Graphics

摘　　要：获得的＂∧＂生长基础的树形结构和森林结构成为有限嵌套层次随机Ｋｏｃｈ曲线岛计算机模拟的基础。定义了３类随机Ｋｏｃｈ曲线岛，并分析了只有周长——面积法才可能得到第２类和第３类曲线岛的稳定分维值。给出了模拟３类曲线岛及其分维值测定的计算程序。从计算结果，明确了实际测定分维和统计维数时应如何选择小岛，所需测量的小岛对数以及分维和统计维数同嵌套层次的关系，３类曲线岛所对应的ｌｇＰ—ｌｇＡ回归直线的分布及其同嵌套层次的关系。The tree and forest structure of '∧' growing bases obtained had made the foundation of computer modeling on random Koch curve island.Three kinds of random Koch curve islands were defined.It was analysed that stable fractal dimension of the second and the third kinds of the above islands could be obtained only from the perimeter area relation.The compute programe modeling the above islands and theirfractal dimension was provided.From compute results,it was cleared that how the islands was selected and the number of island pairs needed in determining of fractal dimension and statistical dimension.The results also showed that both the relationship between fractal dimension (or statistical dimension) and nesteed tier,and the relationship between distributions of regression straight lines of lg P —lg A from three kinds of the islands and nested tier.

关 键 词：随机Koch曲线岛 分维 计算机模拟 金属断口 

分 类 号：TG111[金属学及工艺—物理冶金]