一类非线性分形插值曲面的构造与性质

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一类非线性分形插值曲面的构造与性质

更新时间：2026-09-14

- 一类非线性分形插值曲面的构造与性质
- 一类非线性分形插值曲面的构造与性质
- Issue 1, (2012)
- 作者机构：
  
  太原理工大学数学学院
- 作者简介：
- 基金信息：
- DOI：
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- Published：2012
- 稿件说明：
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姜伟. 一类非线性分形插值曲面的构造与性质[J]. 2012, (1).
DOI：

姜伟. 一类非线性分形插值曲面的构造与性质[J]. 2012, (1). DOI：

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.

Abstract

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.

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