摘要
自然界中存在的许多现象具有分形特征,传统的Euclid空间对具有分形特征的自然界形态模拟具有一定的困难,对此可以用分形插值来拟合自然界形态。基于迭代函数系统（IFS）,通过离散的数据点构成分形插值函数,可以证明分形插值函数是这个IFS唯一的吸引子。分形插值曲线的分形维数直接用数学公式求解比较困难,借助于MATLAB矩阵运算与图形绘制功能,采用图解方法求取,精度可以达到0.01~0.001,从而实现离散数据点的分形插值拟合及其分形维数的求解。试验结果表明,该算法具有简捷直观的特点。
In the nature,many phenomena exists the fractal characteristic,it have certain difficulty to simulate the fractal characteristic nature shape for the traditional Euclid＇s space.Regarding this reason,may use the fractal interpolation to fit the nature shape.Using the discrete data point constructs fractal interpolation function by the Iterated Function System（IFS）,it may prove that the fractal interpolation function is the IFS＇s sole attractor.It is difficult to solve the fractal dimension of fractal interpolation curve by the mathematical formula directly,with the MATLAB matrix operation and the graph plan function,Graphic method is used to solve the fractal dimension,accuracy can reach 0.01 to 0.001,thereby it may realize the fractal interpolation fitting through the discrete data points and solve the fractal dimension.The test result indicated that this algorithm has the simple and intuitive characteristic.
出处
《江西科学》
2010年第2期167-169,185,共4页
Jiangxi Science
关键词
分形插值
迭代函数系统
分形维数
图解法
Fractal interpolation
Iterated function system
Fractal dimension
Graphic method
