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集合分形
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  set fractal
     This paper discusses a basic method for automatic generation of engraving graphics with fractal technique. It introduces the automatic generating procedure with set fractal,function fractal and random fractal,and analysed the factors which effect the generation of engraving grapics with fractal function and the basic translation principle from two-dimensional fractal graphics into tridimensional one .
     该文提出了用分形技术来自动生成复杂雕刻图形的基本方法,并分别介绍了基于集合分形、函数分形与随机分形的雕刻图形的自动生成过程,分析了分形函数生成雕刻图形的影响因素,论述了通过映射实现由二维分形雕刻图形向三维雕刻图形转换的基本原理。
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  “集合分形”译为未确定词的双语例句
     The generating methods of engraving graphics with set or random fractal are put forward in this paper. The engraving graphics can be controlled by the original fractal model,rules of fractal, translation and mapping. With mapping method,the engraving graphics on a plane can be translate into a trimensional graphics on an object with a complex surface.
     提出了用集合分形与随机分形这两种分形方法来创成复杂的雕刻图形,通过控制分形原始模型、分形规则、变换规则或映射规则等,便可实现对雕刻图形的控制.利用映射方法可将二维平面雕刻图形映射到三维雕刻基体甚至更复杂的雕刻基体上,以雕刻出三维以上的雕刻图形.
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  相似匹配句对
     A CLASS FRACTAL SET OF PERFECT DISCONNECTED
     一类完全不连通的分形集合
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     A Fractal Set and Its Properties
     一类分形集合及有关性质
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     The set
     集合(英文)
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     For a set M ?
     对于集合M (?)
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     Random Fractals
     随机分形
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  set fractal
This idea is illustrated in Figure 1, which shows the first three steps to build the Sierpinsky triangle, a well-known point-set fractal.
      


Based on the defination of set fractal a quantitative analysis is made towards the route of "Period-doubling leads to Chaos" by calculecting its fractal measure fractal characteristic number and fractal dimension. It is discovered that the fractal dimension is 0.5 070968…. which is universal when it enters into chaos through Period-doubling.

本文基于集合分形的定义,对“倍周期分支通向混沌”这一途径的分形度量──分形示性数及分形维数进行数值分析,揭示倍周期分支进入混沌时的分形维数为d_Fd_F(X∞)=0.5070968…具有普适性。

Based on Horton law,this paper proposes the property of tip set of branching networks which is more significant in actual works,and the self similar dimension of tip set is obtained.Then multifractal nature of tip set of branching networks with two different branching lenghth ratios is described,and its f(α)~α spectrum as well as D q~q spectrum are analysised qualitatively.Finally,their significance in the real river networks are discussed....

Based on Horton law,this paper proposes the property of tip set of branching networks which is more significant in actual works,and the self similar dimension of tip set is obtained.Then multifractal nature of tip set of branching networks with two different branching lenghth ratios is described,and its f(α)~α spectrum as well as D q~q spectrum are analysised qualitatively.Finally,their significance in the real river networks are discussed.

在Horton定律的基础上提出分枝网络结构的端头构成的集合的分形维数更具有实际意义,并得出了端头集合的自相似维数。在此基础上,又给出了具有两个不同分枝长度比的两分枝结构的端头的多分形描述,并定性地分析了其f(α)~a谱和Dq~q谱。讨论了其在实际河流网络中的意义。

Let {X n,n≥1} be a stochastic process,defined on a probability space (Ω,F,μ),with numerable state space.In this paper,we defined the Box dimension for any set BΩ and studied its properties,obtained another expression for Hausdorff and packing dimension,in the end, we calculated the fractal dimension of a class of subsets.

设{Xn,n≥1}是定义在概率空间(Ω,F,μ)有可数状态的随机过程,给出B的盒维数定义并研究其基本性质,然后得到了集合B的维数的另一种表达式,最后计算了一类集合的分形维数

 
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