复参扰演化系统的分形变形方法研究

Fractal deformation method of complex evolutionary systems under parameter perturbations

为了生成更多具有新型结构特征的分形图,提出了复参扰演化系统的分形变形算法.该算法通过建立含6个扰动控制参数的复参扰演化系统的基本数学模型,采用周期检测法计算复参扰演化系统在给定复平面区域内各离散点的周期值,并根据周期值定义各点的颜色.利用由6个变形控制参数构成的二维变形收缩因子对各离散点进行位置变换,并保持其颜色属性不变,生成最终的分形图.实验结果表明,该算法通过扰动控制和变形控制共12个参数的引入,实现了对复动力系统分形集整体结构和局部细节的有效控制,且算法具有简单、快速和可控强的优点.

To create much more fractals with new type of structures, a fractal deformation algorithm of complex evolutionary systems under parameter perturbations was proposed. An elementary mathematical model of complex evolutionary system under six parameter perturbations was put forward. According to their periodicities counted by period-checking method, the color of every discrete point in the given complex plane was defined. A two-dimensional deformation extension factor in the form of six-parameter family was presented. After the positions of every discrete point were changed by the 2D extension factor while their color properties were kept unchanged, the final fractal images were generated. The experimental results show that the algorithm can expediently control the integral structures and local details of the fractal sets generated from complex dynamical systems when 12 perturbative and deformation parameters are interactively adjusted. The algorithm is simple, fast and easy to control.