递归分形插值曲面的变差

doi:10.3969/j.issn.1000-1565.2016.04.003

河北大学学报(自然科学版) ›› 2016, Vol. 36 ›› Issue (4): 349-352.DOI: 10.3969/j.issn.1000-1565.2016.04.003

递归分形插值曲面的变差

张文景,冯志刚

收稿日期:2015-06-25 出版日期:2016-07-25 发布日期:2016-07-25
通讯作者: 冯志刚(1962—),男,江苏常州人,江苏大学教授,主要从事分形几何理论的研究.E-mail:zgfeng@ujs.edu.cn
作者简介:张文景(1988—),女,江苏徐州人,江苏大学在读硕士研究生. E-mail:656780786@qq.com
基金资助:
国家自然科学基金资助项目(51079064)

Variation of recurrent fractal interpolation surface

ZHANG Wenjing,FENG Zhigang

College of Science, Jiangsu University, Zhenjiang 212013, China

Received:2015-06-25 Online:2016-07-25 Published:2016-07-25

摘要/Abstract

摘要： 在求解函数图像维数过程中,分形插值函数的变差可以代替盒维数公式中最少盒子数,从另一个角度得到函数图像的盒维数公式.从研究二元连续函数的变差性质入手,给出了矩形区域上递归分形插值曲面(RFIS)的变差估计,为递归分形图形维数的研究提供一种新方法.

关键词: 二元递归分形插值函数, 二元连续函数, 分形插值曲面, 变差

Abstract: To calculate the dimension of grap of function, the minimum boxes can be replaced by the variation of fractal interpolation function, and the box-dimension formula can be proved from another angle.Based on the study of the properties of variation of bivariate continuous function,the variation of recurrent fractal interpolation function is estimated on the rectangular domain,which provides a new method to study dimension of recurrent fractal graph.

Key words: bivariate recurrent fractal interpolation function, bivariate continuous function, fractal interpolation surface, bivariate.

中图分类号:

O184

张文景,冯志刚. 递归分形插值曲面的变差[J]. 河北大学学报(自然科学版), 2016, 36(4): 349-352.

ZHANG Wenjing,FENG Zhigang. Variation of recurrent fractal interpolation surface[J]. Journal of Hebei University (Natural Science Edition), 2016, 36(4): 349-352.

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递归分形插值曲面的变差

Variation of recurrent fractal interpolation surface

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