两种特殊的变维分形及其在海洋石油领域的应用

Two Kinds of Special Variable Dimension Fractal and Their Applications in the Offshore Oilf ields

讨论2种特殊的变维分形:分形中的分形与分形中的高阶函数。原有的分形(一阶分形)模型为:N=C/rD;如果D=C′/rD′,则出现分形中的分形或二阶分形。用同样方法可以定义更高阶的分形。类似地可以定义高阶函数(函数中的函数),例如原有的正弦函数(一阶正弦)为:N=sin(kr+b);如果k=sin(k′r+b′),则出现正弦函数中的正弦函数或二阶正弦函数。用同样方法可以定义更高阶的正弦函数。当分形模型中的D值等于高阶函数时,则出现分形中的高阶函数。文中用实例讨论了分形中的分形与分形中的高阶函数的应用。

Two kinds of special variable dimension fractal are discussed in this paper, i. e. , fractal in fractal and high order function in fractal. The existing fractal mode (one order fractal) reads: N = C/rD, in case D = C'/rD , then the fractal in fractals or two order fractal is given. With the same method, the higher order fractals can be defined. Similarly the high order function (function in function) can be defined. For example, the existing sine function (one order sine) reads: N = sin(kr + b), in case k -sin(k'r + b'), then the sine in sine or two order sine is given. With the same method, the higher order sine functions can be defined. In the fractal model, as the value of D equals the high order function, then the high order function in fractal is presented. The examples given in this paper presents the applications of fractal in fractal and high order function in fractal.