The effects of moisture content and spherical shaped silica filler concentration on the resultant tree growth characteristics are explored using Euclidean and fractal geometries. A nano-composite material of MgO added LDPE was subjected to electrical treeing breakdown investigation, as well. As results, the filler particle would create such an obstruction to the tree propagation even if the specimens were moisturized. Moisture would weaken the dielectric strength of resin and the interface. From fractal dimension analysis, it is shown that the complexity of composite structure is followed by the complexity of tree structure. The complex structure of tree is also heterogeneous as quantified by lacunarity. Filler would act as physical barriers to prevent the extension of trees, resulting in higher tree inception voltage and time to breakdown. The more nano-filler concentrations, the longer time needed to make the tree channel diameter thicker enough for breakdown to occur. However, if the diameter is enlarged until about 250 ?m, the effect of nano-filler seemed to be weaker, as shown by simulated tree channel.