迭代函数系统（IFS）是定义和描绘分形的有效方法，每个IFS确定了唯一一个称为吸引子的分形，随机迭代算法虽然能够简单快捷地在计算机上构造IFS的吸引子，但是不能保证在有限步内计算出组成吸引子的所有点，针对这一不足，利用IFS吸引子局部间具有的相似性，提出了由IFS中可逆仿射变换的不动点来逐步生成吸引子的原理和方法，实验证明，该算法是可行的，它不仅能在有限步内生成整个吸引子，并且不必引进概率。

Iterated function system(IFS) is an effective method to define and describe fractals. An IFS determines only one fractal which is called attractor. Although random iterated algorithm proposed by Barnsley can display easily and quickly an attractor of IFS on computer screen, it is not sure to generate all points of an attractor within any limited steps. In order to overcome the shortcoming of the algorithm, a new algorithm of gradually computing IFS attractor from one fixed point of an invertible affine transformation is presented. Because of self_similarity of an attractor of IFS there exists similarity between different regions of an IFS attractor, With this property different parts of an attractor can be showed one by one. The experimental results prove this method is feasible. A whole attractor can be computed through limited steps by using this algorithm, and unlike random iterated algorithm probability is not necessary.