【作者】 毛军军； 张铃； 郑婷婷； 吴涛；

【Author】 Mao Junjun1,2,Zhang Ling2,Zheng Tingting1,2,Wu Tao1,2 1.School of Mathematics and Computational Science of Anhui University,Hefei 230039,P.R.China 2.Key Lab IC&SP,Anhui University,Hefei 230039,P.R.China

【机构】 安徽大学数学与计算科学学院； 安徽大学计算智能与信号处理教育部重点实验室；

【摘要】 本文讨论分形几何与商空间理论的关系,提出商分形的概念,并讨论分形图的逼近与商空间粒度计算之间的关系。得到的主要结论:①证明一个函数迭代系统W={(X,d),wi,i=1,L,n}对应于一个分层递阶商空间链{Xk,k=1,2,L},并给出商空间链{Xk,k=1,2,L}对应的距离函数。②给出Xk上的商映射Wk和商集Pk的构造方法,证明Pk是Wk在Xk上的不变子集。③给出商分形模型的定义和结构:{(Xk,Wk,Pk),k=1,2,L}。④给出Xk到原空间的嵌入方法,证明{Pk}在原空间按豪斯道夫距离收敛于P(P是W的不变子集)。⑤给出函数迭代系统能产生分形图的充要条件。更多还原

【Abstract】 In this paper,the relationship between theory of fractal geometry and theory of quotient space is discussed and a new model which combines the character of granularity and fractal is put forward.Furthermore,approaching to fractal graph with quotient granularity is investigated.Some conclusions are proved separately.①Given a function iterative sys- tem{ X ,wi ,si ,i = 1,2,L ,n},a hierarchical structure { X k,k = 1,2,L} can be proved,and the distance is induced on the quotient chain{ X k,k = 1,2,L} .②Given quotient mapping Wk and quotient sets Pk on X k,then Pk are proved to be invariable sets on X kalong with Wk .③The model of Quotient-Fractal {( X k ,Wk ,Pk ),k = 1,2,L} is constructed.④Lay X k into primary space,{P k } are proved that converge to P with Housdoff distance.⑤a sufficient and necessary condition which performed from a function iterative system to fractal graph is proposed.更多还原