对称性非线性迭代函数系统的分形、分歧及混沌现象

Fractals, bifurcation and chaos generated by symmetric nonlinear iterated function systems

描述一类具有对称性的非线性迭代函数系统所产生的对称性增加的分歧及对称混沌吸引子现象这样的对称混沌现象体现了有序的对称性与无序的混沌性质的高度统一由此类对称的非线性迭代函数系统所生成的图形具有原对称的迭代函数系统一样的对称性，因而可以产生很漂亮的图案。

The symmetry increasing bifurcation and symmetric chaos in nonlinear iterated function systems are described. Such a symmetric chaotic phenomena shows the fine combination of ordered symmetry and disordered chaos. The figure produced by such a nonlinear iterated function system has the same symmetry as the considered iterated function, and is therefore very beautiful and could provide another approach for designing beautiful patterns.