【摘要】 应用分形插值方法可以模拟出预先给定的不同粗糙度的分形曲线和曲面,它能够更好地刻画出自然界中普遍存在的处处不光滑的连续形貌 作为研究函数性态的重要方向,讨论了分形插值函数的积分问题,引用数学归纳法证明了有关分形插值函数在不同尺度下积分问题的几个结论,指出了在不同的尺度下分形插值函数的积分值与生成分形插值函数的变换系数之间的关系,为进一步研究分形函数的小波变换和小波分析提供了基础更多还原

【Abstract】 By using fractal interpolation method, fractal curves and surfaces of given roughness can be imitated. It can better portray the continuous but nowhere smoothing patterns that exist everywhere in nature. The integration of the fractal interpolation function(FIF) is discussed. Some results about integration of FIF on various scales are proved by mathematical induction. The relations between the integration of FIF on various scales and the coefficients of the mappings generating FIF are given.It provides a basis for research of wavelet mapping and wavelet analysis on fractal function.更多还原