A chaotic tree modeling based on discharge currents

Trees are very important objects for studying solid insulating materials, and the modeling urges rapid progress for aging problems. In this paper the Takens´s reconstruction theory used in chaotic studies was applied to the discharge current pulses accompanied with trees developing from the needle tip of a needle-plane electrode system constructed in PE. The tree patterns obtained were photographed simultaneously with the measurements of the discharge currents. The dynamic current attractors are obtained based on Takens´s theory and are gradually extended depending on tree developments. The attractors are composed of two components corresponding to the current polarities. Fractal analysis is also carried out for the attractors to discuss chaotic properties. The relation between the number of square coverings and one side length of the coverings is linear and the representative fractal dimension is approximately 1.46. Thus, the attractors have a chaotic property, and are considered to be a kind of dynamic tree modelings