Multifractal analysis of lightning channel for different categories of lightning

A study from the point of view of complex systems is done for lightning occurred at Diamantina, Sete Lagoas and São José dos Campos, during the summer from September 2009 to April 2010. For the first time, multifractal analyses were performed for different lightning categories: two-dimensional, three-dimensional, non-branched, branched, cloud, cloud-to-ground, single and multiple. We found that when using two-dimensional images of natural lightning embedded in three dimensions to perform multifractal analysis, the interpretation of the multifractal spectrum must be restricted to identification of the multi (mono) fractal character of lightning channel and to estimation of fractal dimension. We have also observed that, on the average, each category has a specific value of fractal dimension. Categories in which branches and tortuosity are more usual, like branched and cloud categories, exhibited largest fractal dimensions due to more complexity of lightning channels. The results suggest that single and multiple lightning have similar complexities in their channels, leading to the same average values of fractal, information and correlation dimensions for both categories.