摘要
讨论了二元连续函数振幅与变差的性质,并构造了一类非线性多参数迭代函数系;证明了在一定条件下吸引子的唯一性和分形插值曲面的存在性,利用连续函数变差的性质研究了所构造的分形插值曲面的维数,并给出了此类分形插值曲面计盒维数的计算公式.
The properties of amplitude and variation of the binary continuous function was discussed,and a class of nonlinear iterated function system of multiple arbitrary parameters was constructed.The uniqueness of the attractor and the existence of the fractal interpolation surface was proved under certain conditions.By using the properties of variation of the continuous function,the box-dimension of the constructed fractal interpolation surface was studied and the calculation formula of the box-dimension was given.
出处
《中北大学学报（自然科学版）》
CAS
北大核心
2012年第1期56-59,共4页
Journal of North University of China(Natural Science Edition)
关键词
非线性迭代函数系
分形插值
连续性
变差
维数
nonlinear iterated function system
fractional interpolation
continuity
variation
box dimension
