分形图形的计算机绘制论文,分形图形生成研究

分形图形的计算机绘制论文,分形图形生成研究

文档介绍：

分形图形生成研究

摘要

分腹F∽tal)是¨二十I趾纪新出现的隶属非线性领域的一个分支学科,它使传统数学中无法表达的形态如山脉、树术等得以逼真的表达。分形几何学在图象数据压缩、模拟自然景观、艺术图案设计、分形生长以及混沌动力系统的研究等方面肯着广泛的应用,并已m现许多研究成果。

m分形迭代函数系统(IFS)的各种算法,依据IFS码生成了Sierpinski二角形、分形Lij、分形树、三维树叶、果斟等各种分形图。而其反问题,即如何从已知图形或已有概念、轮廓中产生、获取[P8码则更为重要,冈此,对IFS绘制图形的特性进行研究以及引陇II喝迭代规律即分形图形生成规律是{‘分必要的。为此,论文薛先通过对]FS码盼实验分析,将树叶迭代码‘j三角形迭代码之问逐渐缩小差距,实现r幽树叶过渡到三角形的一些巾间演变图形。其次,针对同一IFS迭代码两次迭代绘制得到的分形图并非完全相同这一问题展开研究,提出了IFS分形覆盖相交交点变化曲线的概念,给出了覆盖相交交点变化曲线的绘制算法,在此基础上进一步研究了分形覆盖相交交点变化f}}1线的变化率情况,得到了分形覆盖相交交点变化曲线宏观卜比较光滑,但实际上小范围内异常波动的实验结果。最后,用.Julja集的思想实现r多幅艺术图案的设计‘j绘制,并将绘制的多种分形图进行_r综合运用,实现了虚拟景观的生成。

关键词:分形:迭代函数系统lFs;IFs迭代码;JuI ia集

分形圈形生成研究

Abstrct

I:ractal i s a 13ew br-a13ch()r the Reieace form the area of nenlinear in the tw013 Y century.which can express such as mountain,ttee and SO on lifel ike— l y that can’t be expressed in the tradi L f onal mathematics.Fracta】i S widel y limed i n many rj c l ds much as the i mage press i on,simul ation of natural scenery.J;ractal ry’s growing and the researcher of chaos metjlity system and SO 013.

Based on IFS codes and the algorithm of[FS.the fractaj pictures of Sierpinski triangle,fractal mountain,fractal LFOO,three—dimensional teaves, orchard and SO on are simulated by VB programming.But the reverse question j s mere important,that iS,to obtain IFS coder from that have a1 ready exsited image, concept ion or outlined.Therefore,j L is very necessary to research the characteri sti c and look for the iterated regulation of IrS.Firstl Y.by the experl'mel3t and analysis,the fractal images are realized between the tree and the trial39Ie through contract the di ce of their IPS codes gradualIy. Second l Y.f t i S not the same fractal diagram by the same codes of IFS to produce fractal diagram.The two graphs are extraordinary sim[1ar,but they are different in detafl.’rhe promem js researched and tile algorithm which calculales the

i ntersection poi nts of two graphs created by the same coefficient of‘the IFS is

proposed.The curve described changing ot’th

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