一种确定IFSP中迭代次数下限的算法

Algorithm for determining the lower limit of the iterated times in IFSP

提出了一种求解带概率的迭代函数系统(IFSP)中迭代次数下限的自动算法.该算法基于一个基本假定,从给定的多个压缩仿射变换矩阵的谱半径入手,先分别求出每一个压缩仿射变换收敛到其对应的不动点时的迭代次数,然后根据每一个压缩仿射变换使用的概率即可计算出IFSP中迭代次数的下限.理论分析和实验计算结果表明,提出的算法能有效地确定IFSP中迭代次数的下限,且在保证分形图质量的同时避免了不必要的计算开销,为快速生成高质量的分形图提供了一种有效的方法.

From the spectral radius of the given contrastive affine matrixes, the iterated times through which each affine transformation is converged to its fixed point were worked out. Then according to the probabilities that belong to each transformation respectively, we can determine the lower limit of the iterated times for iterated function system with probability （IFSP）. The theoretical and experimental results show that our algorithm can minimize the computational cost while at the same time the quality of the fractal is also ensured. Therefore, the algorithm provides an effective method to determine the lower limit of the iterated times in IFSP, and can generate the fractal object with high quality in the shortest time.