修改Koch曲线岛的迭代二叉树及分维测定

Iterative Twofork Tree and Fractal Dimension Determination for a Modified Koch Curve Island

获得了修改Ｋｏｃｈ曲线岛周界和面积的迭代二叉树，并由之导出了周长和面积的表达式。说明周长—最大直径方法可获得该分形结构分维理论值，同时确定由周长—面积方法获得分维理论值和满足图象分析精度要求的理想分维值的临界嵌套层次及其同参量ａ和ｎ的关系，并认为在分维测定中周长—面积方法是可能得到理想分维值的有效方法。

The iterative twofork tree of perimeter and area on a modified Koch curve island is acquired,and from this, the formulae for calculating perimeter and area is obtained.It shows that the theoretical value of fractal dimension could be acquired from perimetermaximum diameter relation for the fractal structure.It also shows the relation between that the critical nested tier of both the theoretical value of the fractal dimension and the ideal value of the fractal dimension,which meets the precision of autoimage analysis obtained from perimeterarea relation and parameters a and n could be ascertained. It is considered that the perimeterarea method is effective to obtain ideal value of fractal dimension in determenation of fractal dimension.