Fractal characteristics of real electrical trees

The fractal properties of 2-D projected electrical trees in PMMA (polymethyl methacrylate) and XLPE (cross-linked polyethylene) samples have been investigated. The results show that the tree structures are fractal objects although their tree patterns are obtained in a 2-D projection. The fractal dimension of the tree formed in PMMA is found to become constant as the applied voltage or the time duration is increased. Furthermore, the fractal dimension of the tree structures produced in XLPE is found to increase with increasing cross-linking of XLPE. It is concluded that there exists a relationship between the fractal dimension of the electrical trees and the physical properties of the polymers used.<
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