Fractal patterns in nature and feelings

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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.