广义Julia集的非线性复映射族生成模拟

摘要

研究了非线性复动力系统生成广义Julia集的空间分形可视化问题.首先,对于复迭代映射族z←F(zw)+c(w=α+βi)(其中F(zw)为任一复变多项式),定义适当的数据结构存储相关信息；然后,分别基于牛顿迭代、逃逸时间和陷阱分形三种算法的基本思想,并结合色彩学原理,提出计算机模拟非线性复映射族生成一类广义Julia集的具体步骤.大量造型新颖、结构精细、色彩丰富的分形仿真图形不仅验证了算法的有效性,而且为产品防伪标志的创新设计提供了广阔的应用前景.%This paper researched on the fractal visualization issues of the nonlinear-complex dynamic system creating the generalized Julia sets. First of all, it defined the appropriate data structure for saving the iteratively complex mapping family: z←F(zw) +c(w = α +βi) , among which F(zw) standed for the either complex polynomial. Then, respectively basing on the fundamental idea of the Newton-Raphson, time-escaped and trap fractal algorithms while combining the elementary theory of chromatics, it proposed the specific method of the computer modeling the nonlinear-complex mapping family generating the generalized Julia sets. The lots of fractal simulation graphics, which were original pattern and delicate structure and rich coloration, not only verified the algorithms efficiency but also provided the extensive prospect to innovative designing the product's anti-counterfeiting marks.