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對復動力系統(tǒng)理論作出了重要的貢獻,其中之一就是對二次多項式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引進了一種強有力的方法??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,討論了高次多項式的隨機復動力系統(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式函數(shù)的mandelbrot集。
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 本文運用分形理論實現(xiàn)多種分形算法,在計算機上生成mandelbrot集,julia集,l系統(tǒng),ifs迭代函數(shù)系統(tǒng)等典型的分形圖形,同時運用真彩色及調(diào)色板技術(shù)豐富圖形的色彩,實現(xiàn)了色彩動畫,使其更真實的模擬自然景物;運用鼠標編程技術(shù)實現(xiàn)對圖形局部的放大和縮小,體現(xiàn)分形圖形的自相似性和無限延展性;提供多組參數(shù),利用分形圖形的混沌特性,通過微小的參數(shù)變化,生成完全不同的分形圖形。