Fractal patterns in nature and feelings

据报道，许多自然图案和物体都是分形的。分形的投影通常是人们感兴趣的，或者可以通过实验进行研究。拍摄了树木枝叶和花瓣的空间分布，并使用轮廓投影仪精确跟踪了图像。使用计算机辅助CCD照相机系统或图像扫描仪将所描绘的图案数字化为1024 X 1024像素。用计盒法检验了模式的标度不变性。研究发现，秋季的秋红叶、樱花开花和红（黄）叶的二维投影在2个尺度上具有分形性质。由30名志愿者选出的三幅最美丽的风景照片进行了分形分析，发现它们在很宽的长度尺度上表现出尺度不变性。因此，自然图案的尺度不变性可能与我们在观察它们时的美感和/或舒适感有关。我们还应用了一种新的方法，通过测量脑电图（EEG）来检测我们的感觉或情绪。该方法通过FFT分析，预先生成一组情绪（愤怒、喜悦、悲伤、紧张、放松等）脑电频谱数据库。在此基础上，对特定条件下的脑电频谱进行了分析。该方法在自然美观察者脑电分析中的应用正在进行中。

A number of natural patterns and objects have been reported to be fractal. It is often the projection of fractals which is of interest or can be studied experimentally. The spatial distributions of tree branches, leaves and petals were photographed, and the pictures were traced accurately using a profile projector. The traced patterns were digitized into 1024X1024 pixels using a computer assisted CCD camera system or a image scanner. The scale invariance of the pattern was tested by the box-counting method. The 2-dimensional projections of Keyaki leaves, Sakura blossom and red (yellow) leaves of autumn have been found to show a fractal nature over 2 orders of scale length. Three photographs selected as most beautiful scenery by thirty volunteers were subjected to the fractal analysis, and they have been found to show scale invariance over a wide length scale. Thus, the scale invariance of natural patters might be related to our feelings of beauty and/or comfort when observing them.We also applied a new method to detect our feelings or emotion by measurement of electro-encephalogram (EEG). In this method, a set of data-base of EEG spectrum for emotion or feelings (anger, delight, sadness, stress, relax etc) for individual person was pre-created by the FFT analysis. Measured EEG spectra under specific condition were then analyzed based upon the data-base. The application of this method to the analysis for the EEG of person viewing natural beauty is in under way.