given the name “ fractals ” by their discoverer, benoit mandelbrot, the new forms looked nothing like traditional euclidean shapes 這種圖像與傳統(tǒng)歐氏空間中的形體有天壤之別,它們的發(fā)現(xiàn)者曼德布洛稱之為碎形。
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 分形理論作為二十世紀(jì)七十年代世界科學(xué)的三大發(fā)現(xiàn)之一,自其產(chǎn)生之日起就在包括地理學(xué)在內(nèi)的眾多學(xué)科領(lǐng)域中取得了較為廣泛的應(yīng)用。
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 cyoccoz對復(fù)動力系統(tǒng)理論作出了重要的貢獻(xiàn),其中之一就是對二次多項(xiàng)式pc(z)=z~2+c的julia集和mandelbrot集m的局部連通性的研究。在他的工作中,yoccoz引進(jìn)了一種強(qiáng)有力的方法??拼圖技巧。
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個函數(shù)的特定迭代序列,討論了高次多項(xiàng)式的隨機(jī)復(fù)動力系統(tǒng)的julia集的連通的充分必要條件以及稠密性問題,同時還討論了一類多項(xiàng)式函數(shù)的mandelbrot集。
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 本文回顧了分形理論的發(fā)展歷史和現(xiàn)狀,介紹了b.b.mandelbrot分形理論以及圖像分割的基本概念,比較了圖像的幾種分形模型以及適用性能不同的分形維數(shù)計算方法,提出了一種新的計算分形維數(shù)的變尺度差分盒維法。