Given the name “ fractals ” by their discoverer , benoit mandelbrot , the new forms looked nothing like traditional euclidean shapes 这种图像与传统欧氏空间中的形体有天壤之别，它们的发现者曼德布洛称之为碎形。
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Mandelbrot b . b . enunciated the uncertainty of the length of a coastline in his paper " how long is the coastline of british ? " published in " science " in 1967 . the fractal concept was presented for the first time in that paper and has been applied to many fields ever since 分形理论作为二十世纪七十年代世界科学的三大发现之一，自其产生之日起就在包括地理学在内的众多学科领域中取得了较为广泛的应用。
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At the end of the last century , c . j . yoccoz is made significant contributions to the theory of complex dynamics , one of which is the study of the local connectivity of the julia sets of quadratic polynomials pc ( z ) = z2 + c and the mandelbrot set m . in his work C yoccoz对复动力系统理论作出了重要的贡献，其中之一就是对二次多项式pc ( z ) = z ~ 2 + c的julia集和mandelbrot集m的局部连通性的研究。在他的工作中， yoccoz引进了一种强有力的方法? ?拼图技巧。
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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。
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This paper analyze the basic character clutter and the clutter model . it study a simulation algorithm of airborne pd radar and carry out the the clutter sample of different distributing , the location of character clutter in detecting and the relation of radar system parameter are research in this paper 并研究了特征杂波在检测域中的位置与雷达系统参数的关系;介绍了分形技术的发展和基本的mandelbrot分形理论,分析了杂波的分形特征,研究了多重分形技术在杂波跟踪中的应用。
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In the dissertation , author reviews the developed history and presents situation of fractal theory , and introduces mandelbrot " s theory of fractal and primary conception of image segmentation , makes a comparison among some fractal models and some methods to acquire the fractal dimension of a image in complexity and applicability , advances a kind of new differential box counting ( dbc ) method , in which scale of box is variable adaptively 本文回顾了分形理论的发展历史和现状，介绍了b . b . mandelbrot分形理论以及图像分割的基本概念，比较了图像的几种分形模型以及适用性能不同的分形维数计算方法，提出了一种新的计算分形维数的变尺度差分盒维法。
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This paper introduces principle of fractal and the mandelbrot fractal theory . it analyze the fractal character and study the mltifractal for the clutter tracking . in according to the rage which follow the q on point fractal dimension and region fractal exponent . we confirm the prepreerence multifractal high moment , combining the clutter feature of pd radar and novel multifractal approach , the mainlobe clutter tracking come true 以单点分形维数和区域分形指数随q值的变化程度为标准,确定了多重分形最优高阶矩数,结合pd雷达的杂波特性和多重分形算法,实现了主瓣杂波跟踪;研究了贪婪snake方法在杂波跟踪中的应用,介绍了snake基本模型的能量函数,并分析几种常用的snake模型的离散能量函数。
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This paper is devoted to seeking formulas and rules of representation for generating new fractal graphics . the main works are as followed : ( l ) construct new formulas for new fractal aspects after revisited methods for the visualisation of mandelbrot and julia sets based on ifs , we described the other new formulas originating from z z2 + c . including norton and polynomials iterated function , which have integer index instead quadratic index , we also constructed formulas with complex number index . 3 - d dynamical system is discussed then . besides the most widely used sequential visualisation methods , we designed two methods to change the original vectors and get new graphics with special effects 在对公式指数的推广中，包括指数为整数的牛顿迭代法和多项式迭代法，还包括指数为复数的迭代公式；在离散动力系统的吸引子生成算法讨论中，将复数z向高维空间推广，重点论述了生成了三维离散动力系统吸引子的收敛条件，实现了此吸引子对应的三维空间向量在平面上的投影图的条件；还讨论了迭代前对初值点进行两种不同变换对得到的分形图形的影响，以及这两种变换组合图形的生成。
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In virtue of the knowledge related to fractal theory , all fractals algorithms in the paper have already been realized on computer , such as mandelbrot sets , julia sets , l system and iterated function system , etc . and their fractal figures have been drawn . meanwhile , to obtain a better visual effect and simulate actual natural scene , software adopts the real color and color palette to enrich figures , and color animated cartoon to change them . to show the self - similarity and infinitive tractility of fractal figures , partial zoom has been made on them 本文运用分形理论实现多种分形算法，在计算机上生成mandelbrot集， julia集， l系统， ifs迭代函数系统等典型的分形图形，同时运用真彩色及调色板技术丰富图形的色彩，实现了色彩动画，使其更真实的模拟自然景物；运用鼠标编程技术实现对图形局部的放大和缩小，体现分形图形的自相似性和无限延展性；提供多组参数，利用分形图形的混沌特性，通过微小的参数变化，生成完全不同的分形图形。
