迭代函数系统分形图覆盖相交曲线及其变化率的研究  

Research on the intersection property of the graphs created by the same coefficients of iterated function system

作　　者：于万波[1] 袁宝民[2] 魏小鹏[1] 

机构地区：[1]大连理工大学机械学院 [2]石油大学机电工程学院,山东东营257061

出　　处：《石油大学学报（自然科学版）》2004年第2期82-84,共3页Journal of the University of Petroleum,China(Edition of Natural Science)

基　　金：国家自然科学基金资助项目 ( 60 1740 3 7;5 0 2 75 0 13 );国家"863"项目 ( 2 0 0 1AA412 0 11)

摘　　要：针对用随机线性迭代函数系统 (IFS)迭代时同一迭代码在两次有限迭代中得到的分形图并不完全相同的问题进行了研究 ,提出了IFS迭代分形覆盖相交交点变化曲线的概念 ,给出了覆盖相交交点变化曲线的绘制算法 ,在此基础上进一步研究了分形覆盖相交交点变化曲线的变化率。结果表明 ,分形覆盖相交交点变化曲线宏观上比较光滑 ,但实际上会在小范围内发生波动。该研究结果对数据表示。Two graphs in the plane drawn using the same coefficients of the iterated function system (IFS) are different. A new drawing algorithm was proposed. The intersection points of the two graphs drawn using the same IFS coefficient can be calculated by means of the algorithm. The method for drawing the curves describing the change of the intersection points was given. The result shows that the curve is smooth when it is seen as a whole and fluctuates remarkably in the tiny range. In fact,the curve is a fractal one. These results can be used in the data model and concept construction.

关 键 词：迭代函数系统 IFS 迭代码 覆盖相交 域值 高斯函数 混沌分形 

分 类 号：O415.5[理学—理论物理]