The impact of laser fluence and pulse duration on both the rate and probability of growth of laser-induced damage sites has been reported and analyzed statistically in a companion paper. In this paper, we report and analyze the volume morphology of damage sites during the growth process in fused silica optical components, at 351 nm, under various laser fluence and pulse durations. Fractal analysis has been used to quantify the bulk damage morphology. A clear link between the damage morphology and laser pulse duration has been observed. The results from fractal analysis allows for a better understanding of the results from the stochastic approach developed in our companion paper. More specifically, fractal analysis shows how the laser parameters such as fluence and pulse duration impact the phenomenology and the dynamics of the growth process.