Mandelbrot set

Studies on Printing Pattern Design Based on Triangle Function Mandelbrot Set

基于三角函数Mandelbrot集的印花图案设计初探

Application of Higher Degree Power Mandelbrot Set Patterns to Fabric Pattern Design

高次幂Mandelbrot集艺术图形在纺织设计中的应用

Studies on fabric patterns designing with visual information in Mandelbrot set

纺织设计中Mandelbrot集可视化信息表征方法的研究

Two Methods of " Mandelbrot Set " Implemented in Network Parallel Environment and the Comparison Between Them

网络并行环境下MandelbrotSet图形的两种实现方法及其比较

The representation of some internal structures of the Mandelbrot set

Mandelbrot集内部结构的描述

An Algorithm for 3D Mandelbrot Set Drawing Generation

三维Mandelbrot图形生成算法

The MPI Implementation of Parallel Algorithm About Mandelbrot Set

Mandelbrot集并行算法的MPI实现

Mandelbrot set is an extremely important fractal set . It is generated by visualization methods .

Mandelbrot集图形是通过可视化方法生成的一类非常重要的分形图形。

Visualization of Quaternion Mandelbrot Set and Julia Set and Discussion for Data Transformation in Higher Space

四元数空间M-集与J-集的可视化及高维数据转换的应用探讨

On Constructing Julia Set and Mandelbrot Set in Four-dimensional Space

在四维空间中构造Julia集和Mandelbrot集

Some Internal Structures of the Mandelbrot Set

Mandelbrot集内部结构

In fractal theory , Mandelbrot set and Julia set are all extraordinary complicated objects .

分形理论中Mandelbrot集和Julia集都是非常复杂的对象。

The problem on visualization of quaternion Mandelbrot Set and Julia Set is discussed in this paper .

讨论四元数空间M集与J集的可视化问题；

The algorithm can also be applied in the drawing of other complex fractal pictures such as Mandelbrot set and sierpinski triangle .

该算法同样适用于Mandelbrot集、Sierpinski三角形等其他复杂分形图。

First , a fractal pattern of Mandelbrot set is produced using computer and the pattern is detected by multi-scale fractal parameters with a ideal result .

这里用计算机生成了Mandelbrot集的分形图案，用多尺度分形参数进行了检测，效果显著。

Furthermore , the topological invariance on the periodic buds Fibonacci sequence and golden section point in the Mandelbrot set are discovered .

同时，通过实验与数据分析发现Mandelbrot集周期芽苞的Fibonacci序列的拓扑不变性，找到M集内的黄金分割点。

Consequently , the results are found in the study : ① The Julia set from third-order simplified Newton ' method contains the structure of classical Mandelbrot set ;

结果发现：①三阶简化牛顿变换的Julia集中含有经典Mandelbrot集的结构；

The paper analyses the characteristic of algorithm design in the MPI environment , describes the implementation of three algorithms about Mandelbrot Set in the MPI environment , and comparison in made between them .

分析了MPI环境下算法设计的特点，描述了在MPI环境下实现Mandelbrot集的三种算法，并对它们进行了比较。

Through gradually magnifying the edges of these pictures , it reveals clearly the infinite nesting self similarity and close connection between Julia Set and Mandelbrot Set .

并用C语言编制程序模拟生成分形图象Julia集和Man-delbrot集，通过对其图象的边界进行逐级放大，可以清楚地了解到它们的无限嵌套的自相似性以及Julia集和Mandelbrot集的密切关系。

The Mandelbrot set is infinitely deep and complex at all scales , but a float or a double can go only so deep before losing the ability to distinguish adjacent points .

Mandelbrot集合在各个级别上都是非常细微和复杂的，但是float或double可以在失去区分相邻点的能力之前达到这个细微的级别。

For instance , I 've seen this come up in Mandelbrot set explorers where you can zoom in so far that the entire graph falls between the nearest two doubles .

例如，我曾经在Mandelbrot集合管理器看见过这种情况。在其中可以放大曲线图，让其落在最近的两个双精度数之间。

Based on Yaupon-Exponent , two kinds of chaos model , one is Mandelbrot set , another is Henon mapping , is analyzed . Father more for these two model how to get from orderly state to chaos is studied .

利用李雅普诺夫指数分析了两个复动力系统的混沌模型，一个是Mandelbrot集，另一个是伊侬映射，进而探讨了这两个模型在什么情况下从有序进入混沌状态。

This article is based on the author 's experience in writing fractal-generating program . It describes the math model of typical Julia set and Mandelbrot set , and tells the readers how to generate opposite fractal images ;

基于作者开发分形图形生成程序的亲身实践，主要描述了Julia集和Mandelbrot集这两个最典型的分形集的数学模型，以及如何在计算机上生成相应的分形图形；

In this paper , the fractal feature of the Mandelbrot set is discussed . The algorithm of generating 3D Mandelbrot set graphics based on 3D continuous potential method is expounded , and it is extended to generalized Mandelbrot set graphics .

探讨了Mandelbrot集的分形特征，阐述了基于三维连续位势法生成三维Man-delbrot集图形的算法，并将之推广到广义的Mandelbrot集上。

Chapter two study iteration of a serial of polynomial , discussed the sufficient and necessary conditions and denseness of the Julia set , the relative random dynamical system is constructed by some high degree polynomial . In addition , it discuss the Mandelbrot set of a kind of polynomial .

本文的第二章主要研究多个函数的特定迭代序列，讨论了高次多项式的随机复动力系统的Julia集的连通的充分必要条件以及稠密性问题，同时还讨论了一类多项式函数的Mandelbrot集。

A series of M-J chaotic-fractal image families are generated by the escape time algorithm . Universal constant in the Mandelbrot set and approximate scaling invariable factor in the Julia sets are discovered , which qualitatively demonstrate scaling invariance of M-J chaos-fractal images .

利用逃逸时间算法绘制MJ混沌分形图谱，通过计算机数学实验找到Mandelbrot集的普适常数和相应充满Julia集的近似标度不变因子，定性说明了MJ混沌分形图谱标度不变的特性。

To analyze the convergence and structure of the attractive basin and the repulsive basin of the free critical points in the extra fixed points is very important way to study Mandelbrot and Julia set .

分析额外不动点中自由临界点的吸引域的收敛性和结构特征，是用来分析Mandelbrot集和Julia集的重要方法。