Fractal dimension is a statistical index of complexity to characterize geometries. It is commonly used in signal processing in different fields of research. There, observations of dynamic systems can be translated into numerical values allowing us to classify signals into groups of similar characteristics. In full-waveform LiDAR this methodology can be applied to the reflected echo pulse, thus enabling an analysis based on the overall waveform characteristics. Consequently, the fractal dimension of the full-waveform can be leveraged to differentiate between echo pulses with a high number of returns and single- or low-return echo pulses. This introduces an independent measure, which is calculated prior to the signal processing step. The advantage of this initial classification is that the echo pulse extraction could be further improved without need for human supervision, as the correlation between the number of echo pulses and the fractal dimension hints towards a measure of estimating the number of echo pulses within a recorded full-waveform. To conclude, we expand the concept of the fractal dimension to LiDAR waveforms and use the extracted correlation between the number of echo pulses and the fractal dimension to gain new insights for estimating the total number of echo pulses. This improvement is demonstrated through comparisons with manually annotated data, advancing the state-of-the-art in full-waveform analysis and introducing additional parameters.