桂花叶片的分形特征

Fractal Characteristics of Leaves of Osmanthus fragrans Lour

提供了一种叶片分形维数的测定方法,并用其测定了桂花(OsmanthusfragransLour)的叶片分形维数。通过分析发现:(1)桂花叶片具有典型的分形特征并且这种分形特征可以用分形理论的一般方法加以研究;(2)同一株桂花树的成熟叶片在统计意义上具有相同的分形维数;(3)对于桂花这个物种的成熟叶片在统计意义上具有相同的分形维数。由此推测同一种植物的成熟叶片(或者其他构件)具有相同分形维数。最后提出创建植物分形分类学的设想。

This paper offers a method to measure leaf's fractal dimension (FD) by introducing the box-counting dimension, one method the fractal theory provided. The scanned photos of mature leaves are treated according to the box-counting dimension. We use this method to measure the leaf's FD of Osmanthus fragrans Lour. By analyzing the result, we find that: (1) The goodness of linear fit of double-logarithmic plot of the number of boxes to box size is significantly great: all the absolute values of coefficient of correlation are greater than 0.9991 that is very close to 1, the expectation. So we conclude that leaves have typical fractal characteristics, which can be studied by fractal theory. (2) The FDs of all leaves of Tree01 from the sample are between 1.7258 and 1.8880, with an average of 1.8065, a standard deviation of 0.0393 and a coefficient of variation (CV) of 2.7180%, which imply the low discreteness. And all the data are normally distributed as well. Other trees in the sample share the same case, so we conclude that the mature leaves of the same tree have the same FD statistically. (3) The ANOVA using the completely random model shows that the differences between the 10 sample trees are not significant: F=0.706<F(9,490,0.05)=1.899, which means that the mature leaves of Osmanthus fragrans Lour share the same FD statistically. Therefore we presume that the mature leaves (or other module) of the same species share the same FD statistically. Finally we propose an idea of founding plant fractal taxonomy.