一个迭代函数系统的分形混沌特性及其应用

The Fractal and Chaotic Natures of an Iterated Function System and Its Application

介绍迭代函数系统生成分形的原理以及分形位移动力系统的混沌特性.构造了一个迭代函数系统,用于生成充满整个单位正方形的填充曲线,理论上证明该迭代函数系统的分形位移动力系统的Devaney混沌特性.将该迭代函数系统的分形位移动力系统参数化,数值上验证该分形位移动力系统的混沌性能,并使用该混沌系统设计了一个基于DNA运算的混沌图像加密算法,详细分析了该加密算法的安全性.

The principle of generating fractal by iterated function system and the chaotic characteristics of fractal shifting dynamical system are introduced.An iterated function system is constructed to generate the filling curve on the unit square.The Devaney chaotic nature of the fractal shifting dynamical system is proved.The fractal shifting dynamical system is parameterized,and its chaotic natures are verified numerically.Based on the fractal shifting dynamical system,a chaotic image encryption algorithm is designed by combining DNA operations.The security and performance analysis of the cryptosystem are carried out as well.