采用改进的牛顿迭代法的分形艺术图形设计

摘要

Newton-Raphscm method is one of the core algorithms which provide materials in the process of the realization of fractal art images. But there are some deficiencies such as low displaying speed, little varied patterns and difficult controlling in resulting fractal images with Newton-Raphson method. Thus, based on Newton-Raphson method, a modified algorithm of generating fractal images - p-DQDA is proposed in this paper, greatly improving the speed of creating fractal images. And the general Newton iterative approach embedding parameters in the iterative process is also proposed, making it possible to generate a wide range of fractal art images with symmetric beauty by a simple parameter adjustment while drawing fractal images, thus enriching the resource library of fractal images.%牛顿迭代法是为分形艺术图形实现提供素材的核心算法之一,但直接采用牛顿迭代法生成分形艺术图形存在显示速度慢、生成图形种类少、难于控制等不足.提出了一种基于牛顿迭代法生成分形图形的改进算法p-DQDA,极大的提高了生成分形图的速度.同时还提出了在迭代过程中嵌入参数的构造牛顿广义迭代式的方法,使得绘制分形艺术图形时通过简单的参数调节,就能够生成种类繁多的具有对称美的分形艺术图形,丰富了分形图形资源库.