采用牛顿迭代双侧逼近误差序列的分形艺术图形设计

The Design of Fractal Art Graphics Based on Two-Side Approaching Error Series of Newton Iteration

提出解实数方程Newton迭代双侧逼近序列的构造方法,精确解介于两个序列之间,这样可以通过两个近似解来估计逼近精确解的程度,给误差分析带来很大方便。把双侧逼近和误差估计扩展到复域上,根据复域上迭代生成的误差序列并结合着色算法和特效处理算法生成美丽的分形艺术图形。

A two-side approaching series based on Newton iteration method is presented to obtain solution of real functions. The exact solution is located between the two series, so the extent that the approximate solution approached exact solution can be estimated with the two approaching series, and it is convenient to analyze errors. Then the two-side approaching series and error estimations are extended to complex domain. With algorithms of coloring and special effective processing, lots of beautiful fractal art graphics are created based on the error series that are generated through iterations from complex domain.