摘要：研究牛顿迭代法所产生的一系列有趣的现象，其收敛性，收敛原理都是本文研究的重点。本文还重点研究分形理论，利用数学实验的方法，对分形的原理、性质做了深度的探索。随着分形理论的不断发展和应用, 将分形理论用于描述不规则的图形, 已成为目前研究世界物质模型的一个扩展。本文将牛顿迭代法用于绘制分形图形, 其可以生成绚丽多彩的分形图形.

关键词：牛顿迭代法; 收敛性; 分形原理; 分形图形.

Abstract:  The iteration generated an interesting phenomenon of Newton Method. The key of this paper is convergence and convergence theory. And the paper will research the fractal theory, using mathematical method, to do exploration with fractal theory and quality. With the continuous development of fractal theory and application, the fractal theory is used to describe the irregular graphics, has become the physical model of an expansion in present study. To realize the algorithms of creating the fractal graphics with Newton overlapping method, and using MATLAB to draw the graphics of the fractal with computer, so it can generate colorful fractal pattern.

Key words: newton method; convergence; fractal theory ; fractal graphics