Fractal analysis of the tree pattern and the discharge luminescence pattern

The purpose of this study is to analyze the growing process of trees which generate at the pointed tip of the needle void by basing on fractal theory. In the measurement system, the PMMA blocks were using as the insulating material and the construction of electrodes was composed of a needle and a plate. For measuring section, one cycle of the applied voltage was divided into twenty areas of equal phase angle, which were named by φ1, φ2, ..., φ20 in order from the negative peak to the next negative peak of applied ac voltage. The quantitative evaluation of fractal dimension (Df) of the discharge luminescence pattern was performed for every area, particularly, for the areas of φ7, 8 and 9 where the discharge luminescence reach at around the tree tip. It was noted that some samples revealed the tree with significantly different pattern even under the same experimental condition. Then, the causes of the appearance of the different tree have been investigated by determining fractal dimension which seemed to depend on the growing process of tree. When the discharge luminescence at φ7, 8 and 9 with large Df generate, the luminescence with the complex branches generate. These results means that the discharges generated in a 7, 8 and 9 arrived to the tree tip