An estimate of the fractal dimension of water trees

Water trees are regions of microcavitation and filamentary damage in a polymer (such as XLPE) caused by the penetration of aqueous salts and the presence of an electric field. They appear in the insulation of service power cables and can lead to electrical failure. The ramified visual aspect of water trees suggests underlying fractal characteristics. The calculation of the fractal dimension can help to confirm the fractal character and to understand the physical mechanisms that lead to water tree formation and growth. In this paper two types of experimental images of water trees have been investigated: (i) methylene blue stained water tree images obtained with the help of optical microscopy; (ii) images obtained using SEM (scanning electron microscopy)