复变换Z←aZ+t_i在分形构图中的应用  

Application of Plural Transform Z←aZ+t_i in Fractal Composition

作　　者：樊翠芳[1] 林贻侠[1] 

机构地区：[1]上海大学机械电子工程与自动化学院,上海200072

出　　处：《上海大学学报（自然科学版）》2003年第2期139-144,152,共7页Journal of Shanghai University:Natural Science Edition

摘　　要：该文详细阐明了复变换Z=aZ+ti的定义,严格证明了复变换迭代收敛定理及该复变换迭代图形是分形图;提出了分形图局部相切的条件为a=sin(π/n)/[1+sin(π/n)],且当a大于该值时,各局部吸引子相交,小于该值时相离,为分形构图提供了判别依据;文中还详细讨论了在复变换基础上各种变形分形图形的构图规则,并提出了一种新的构图方法.This article givens a definition of the plural transform Z=aZ+ti, and proves the theorem of the plural transform iterated mapping convergence. Several important properties of the plural transform fractal images on the basis of the theorem are presented. Applications to the fractal composition and the searching after fractal composition on the basis of the plural transform are discussed. The paper also provides an useful method for obtaining parameters of IFS and a new approach of the fractal composition.

关 键 词：分形图形 迭代函数系统 复变换迭代收敛定理 复变换迭代图形 构图方法 分形几何学 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术] O415.5[自动化与计算机技术—计算机科学与技术]