几何分形图形的动态方向准则

本文提出了一种新的生成自相似几何分形集的技术准则：动态方向准则，并给出了动态方向准则的应用原则，在该原则下，提出了符号移位法，以实现递归过程中方向的动态 控制。动态方向准则继承了传统方法中生成几何自相似集的机理，同时增加了由一种生成元和初始元所能生成的分形图形的种类。     

一个简单分形图形的实现

分形几何是研究无限复杂但具有一定意义的自相似图形和结构的几何学,在描述不规则的复杂的自然现象、分形理论发挥着越来越重要的作用,最后用分形几何理论画了一棵树并给出了程序。     

以折线为母线的自相似分形图形的程序实现

自相似分形图形是分形图形的重要分支,以折线为母线的自相似分形图形是自相似分形图形的主要组成部分。该文对传统的根据具体母线形状编程画图的方法加以改进,给出了一个程序实现所有以折线为母线的自相似分形图形的作图方法并编写了实现该方法的源程序、源程序经编译连接形成可执行文件后,运行时只需在命令中给出母线数据,计算机便自动获取屏幕尺寸,确定图形大小和位置,然后将图形画出。     

具有平面晶体对称性混沌吸引子的分形极限图

提出用混沌函数构造具有平面晶体群对称性混沌吸引子的上半平面、方极限和圆极限分形图的简便方法.通过确定单个混沌吸引子所在的基本区域,利用同胚仿射变换,把基本区域中的混沌吸引子自相似地映射到上半平面,进而生成方极限、圆极限分形图.这些图案具有很好的艺术渲染力.该方法使单个混沌吸引子保持几何结构不变,但图形在整体上却具有很好分形自相似的性质.     

基于MATLAB的分形仿真研究

研究重点是用MATLAB编程语言来实现分形图形。如应用分形几何学中的IFS系统理论和L系统理论,用MATLAB语言生成具有自相似特征的、精美的分形图案。为地貌描述、生物学的仿真研究、艺术设计等领域提供了新的方法。     

基于OpenGL的分形山三维模拟生成技术

采用OpenGL技术与VC＋＋6.0结合分形几何的方法来模拟绘制三维分形山。利用分形几何理论建立几何模型;依据分形插值理论设计相应的算法,得到模拟对象的几何数据,绘制出三维山和云的图形;利用OpenGL的图形处理及渲染功能对生成的图形进行色彩、光照、纹理等方面的处理,得到三维分形山的模拟图形。     

使用C++ Builder编程演示曼德布罗分形图

分形几何方法在计算机图形学和模拟仿真学的研究中具有重要的应用,而曼德布罗分形图是分形几何中的一个经典实例.阐述了如何使用C Builder编程实现曼德布罗分形图的多级放大与缩小演示,只要将其中分形迭代的算法进行改变,此方法可以对其他的分形图进行多级放大与缩小演示.     

分形几何在计算机图形学中的应用

介绍了分形几何理论的基础以及分形图形的主要生成方法,阐述了分形几何学在计算机图形学中的应用。     

分形与工业设计

文章主要研究了分形的自相似原理在工业设计方法学上的应用和分形图形以装饰的方式在工业设计技法上的应用,其中分形的自相似原理的运用是在该领域的探索性尝试。分形的运用为工业设计领域提供的新思路。     

基于分形几何的真实场景物体表示及应用

介绍了分形维数的概念,对利用自拟似分形和自仿射分形实现分形物体的绘制算法进行了描述。实现了场景中不规则自然景物几何形状的真实感表达。     

A comparison of fractal dimension estimators based on multiple surface generation algorithms

Fractal geometry has been actively researched in a variety of disciplines. The essential concept of fractal analysis is fractal dimension. It is easy to compute the fractal dimension of truly self-similar objects. Difficulties arise, however, when we try to compute the fractal dimension of surfaces that are not strictly self-similar. A number of fractal surface dimension estimators have been developed. However, different estimators lead to different results. In this paper, we compared five fractal surface dimension estimators (triangular prism, isarithm, variogram, probability, and variation) using surfaces generated from three surface generation algorithms (shear displacement, Fourier filtering, and midpoint displacement). We found that in terms of the standard deviations and the root mean square errors, the triangular prism and isarithm estimators perform the best among the five methods studied.     

基于格图像的康托集分维与泛逻辑运算

对康托集的研究一直是分形领域的经典而又热点的课题。本文尝试用一种新的模式——“格图像”来研究康托集的分形特性,给出了康托集的格图像构造与分形维数计算方法,计算表明：康托集的自相似分维是格图像分维的特例,格图像分维是自相似分维的扩展。文章首次在分形领域引入泛逻辑的概念,给出了基于格图像的康托集的泛逻辑“与,或,非”运算模型,它不仅考虑了集合的代数列度大小。而且考虑了在参考格中的几何位置关系,这给分形图像的研究提供了一种新的思路,同时也拓展了泛逻辑学的应用领域。     

Construction and application of fractal interpolation surfaces

Fractal geometry has unique advantages for a broad class of modeling problems, including natural objects and patterns. This paper presents an approach to the construction of fractal surfaces by triangulation. After introducing the notion of iterated function systems (IFSs), we prove theoretically that the attractors of this construction are continuous fractal interpolation surfaces (FISs). Two fast, parallel, and iterative algorithms are also provided. Several experiments in natural phenomena simulation verify that this method is suitable for generating complex 3D shapes with self-similar patterns.Project supported by the National Natural Science of China     

Self-Assembling Rulers for Approximating Generalized Sierpinski Carpets

Discrete self-similar fractals have been used as test cases for self-assembly, both in the laboratory and in mathematical models, ever since Winfree exhibited a tile assembly system in which the Sierpinski triangle self-assembles. For strict self-assembly, where tiles are not allowed to be placed outside the target structure, it is an open question whether any self-similar fractal can self-assemble. This has motivated the development of techniques to approximate fractals with strict self-assembly. Ideally, such an approximation would produce a structure with the same fractal dimension as the intended fractal, but with specially labeled tiles at positions corresponding to points in the fractal. We show that the Sierpinski carpet, along with an infinite class of related fractals, can approximately self-assemble in this manner. Our construction takes a set of parameters specifying a target fractal and creates a tile assembly system in which the fractal approximately self-assembles. This construction introduces rulers and readers to control the self-assembly of a fractal structure without distorting it. To verify the fractal dimension of the resulting assemblies, we prove a result on the dimension of sets embedded into discrete fractals. We also give a conjecture on the limitations of approximating self-similar fractals.     

Fractal interpolation on the Koch Curve

The Koch Curve can be obtained as an iterated function system construction. Self-similar interpolation is possible for any function on the sets that are defined recursively. We prove that the Koch Curve (KC) is an analogue of the fractal interpolation theorem of Barnsley. Also the classical harmonic functions are defined on the KC as the degree 1 polynomials for self-similar interpolation.     

Hindu temples: Models of a fractal universe

Hindu philosophy views the cosmos to be holonomic and self-similar in nature. According to ancient architectural tradition, Hindu temples are symbols of models of the cosmos and their form represents the cosmos symbolically.The procedures and methods used in the construction of Hindu temples bear a striking resemblance to the procedures of computer graphics, including discretization, fractalization and extensive use of recursive procedures, including self-similar iteration. The instructions given in ancient Vastu shastras (texts on architecture) work like general programmes to generate various types of temples.The paper is an attempt to draw attention to the similarities between the procedures and resulting forms in computer graphics and Hindu temple architecture and to explain the relationship that exists between the form of the temple and the concepts of Hindu philosophy. It is proposed that Hindu temples may be viewed as threedimensional fractal models and that the use of fractal geometry procedures has a special symbolic meaning in the generation of the forms of Hindu temples.     

数理统计特征的快速图像分形压缩算法研究

图像自相似是图像分形研究中一个重要的研究方向,尤其是对自相似图像子块的特征提取量化问题尤为引人关注。在分形图像编码发展的过程中,图像自相似特征的提取和量化得到了广泛的研究和应用。通过对图像数理统计特征的研究,提出了一种对图像子块进行分类的方法,使拥有相似特征的图像子块能够划分到更小的区域范围内,改进了分形图像压缩算法。经过分析和实验证明,该方法在不影响重建图像质量的前提下,提高了分形编码的速度,较大程度地减少了计算量。     

无损分形整形器模型及其性能分析研究

在自相似网络入口处利用分形整形器对输入业务流进行监控是实现自相似网络QoS保障和避免拥塞的必要手段。基于网络演算建立了无损分形整形器的数学模型,进而给出了无损分形整形器的性能模型,分析并讨论了无损分形整形器的引入对自相似网络性能的影响。     

Flavor system and message passing as representation of knowledge for solid modeling in CAD expert system

The flavor system and message passing (available in the LISP machine LISP) as a method of representation of knowledge for a solid modeling system can be a part of designing a graphical based expert CAD system. Utilizing the flavor system gives us the possibility to define different models for the same object, mixing them together as one and storing the three classes of information (geometry, topology and engineering) for the object separately so that they can be manipulated independantly, which minimizes the redundancy of data stored. Our experimental system utilizes the combinatorial geometry and “Raycasting” for the generation of the solid images.     

基于OpenGL的分形山三维模拟生成技术

采用OpenGL技术与VC 6.0结合分形几何的方法来模拟绘制三维分形山。利用分形几何理论建立几何模型;依据分形插值理论设计相应的算法,得到模拟对象的几何数据,绘制出三维山和云的图形;利用OpenGL的图形处理及渲染功能对生成的图形进行色彩、光照、纹理等方面的处理,得到三维分形山的模拟图形。