Electrical treeing degradation is associated with partial discharge activity. Here we relate the growth of electrical trees with the correlation dimension of the reconstructed dynamic object obtained from the nonlinear time series of the partial discharges from the tree propagation, and with the box-counting fractal dimension of the resulting 3D structure of the trees. The growth of trees at 8, 10 and 12 kV has been analyzed; different PD dynamics were found, depending on both the voltage and the stage of growth. A lower fractal dimension is shown to be related to a lower correlation dimension. The results show that nonlinear time series analysis can be an alternative method of analyzing tree growth and associated partial discharges.