Mandelbrot集高周期混沌吸引子定位算法研究

Research high-period chaos-attractors locating algorithm in Mandelbrot set

研究Mandelbrot集混沌分形图谱混沌吸引子定位算法。设计高周期混沌吸引子的定位算法,该算法将复平面区域网格化,根据混沌吸引子模值局部最小的特性,确定其坐标位置。针对实轴上混沌吸引子分布密集难以处理的情况,算法将复平面划分为实轴上侧、实轴和实轴下侧三个部分,实轴上的混沌吸引子采用单独的遍历方法进行查找。分析定位算法的算法效率,通过编程实现算法,给出了部分周期的混沌吸引子计算结果。实验结果表明该算法可以快速、准确地计算混沌吸引子的位置坐标。

This paper researched the chaos-attractors locating algorithm of Mandelbrot set fractal patterns.According to revelation escape time algorithm,designed high-cycle locating algorithm for chaos-attractors,divided this locating algorithm to the complex plane into many regional grids.According to the local chaos-attractors modulus of the smallest features,locating algorithm divided coordinate plane into three regions： the real axis region,the top side of real axis and the lower side of real axis,the real axis of the chaotic attractor using a separate algorithm.Analyaed the efficiency of locating algorithm.By programming the system,and gave a part of some cycles chaotic attractor results.The experimental results show that the algorithm can quickly and accurately calculate the position coordinates of chaos-attractors.