Fractal dimension analysis of lightning discharges of various types based on a comprehensive literature review

In this study, photographic records of natural lightning flashes obtained from high-speed video camera observations are analyzed based on an extensive literature review. The purpose of this work is to estimate the fractal dimension of lightning discharges and to analyze and evaluate the effect of lightning type (downward and upward flashes during their propagation as well as return strokes) and lightning polarity (negative and positive). Three methods of fractal dimension estimation are employed namely the: (i) box-counting, (ii) sandbox, and (iii) correlation method, utilizing algorithms developed in MATLAB software. Appropriate image processing techniques are employed to guarantee precision in fractal dimension estimation. A thorough discussion is conducted by comparing the estimated fractal dimension values with those previously documented in the relevant literature based on field observations. The mean fractal dimension of downward negative leaders for the three methods (1.18, 1.31, 1.38) aligns well with previous studies, while positive downward leaders exhibit lower values (1.08, 1.15, 1.26), denoting a reduced branching behavior; upward leaders demonstrate slightly higher fractal dimensions than downward ones. Additionally, an attempt to correlate the lightning return stroke peak current with the fractal dimension is made. The outcomes of this research may assist in facilitating precise modeling of the lightning attachment phenomenon, thereby contributing to the development of safer lightning protection systems.