不同判敛标准间的关系及一种构造分形的加速算法

Relations among Different Criteria for Convergence of Iteration and An Accelerated Fractal Construction Algorithm

摘要: 函数迭代产生的美丽、奇异的分形图案依赖于收敛标准的制定,用什么样的收敛标准判定迭代的收敛,对构造分形集起着决定性的作用.文中利用计算机实验数学的方法,结合理论讨论了几种收敛标准的等价性,构造了不同方法的分形图;并通过新的收敛标准给出了一种构造分形的加速算法.

Abstract: Beauty and complexity of the patterns resulting from the iteration of mathematical functions depend on the criterion for convergence. The authors study the equivalence of several criteria for convergence and construct their fractal patterns by the method of computer experimental mathematics. A new accelerated algorithm is given by means of a new criterion for convergence of iteration.