Fractal analysis: Pitfalls and revelations in neuroscience

Fractal analysis has become a popular method in all branches of scientific investigation including ecology, physics and medicine. The method is often used to determine effects such as impact of cattle grazing, the distribution of stars within a galaxy or whether tissue is pathological. However several aspects of fractal analysis are not often considered when interpreting results communicated in the literature. These include the concept that no presentation of any pattern on a computer, even for an ideal fractal, is truly fractal. Pre-processing that is also required, such as scanning of images and resizing play a role in the variation of the final fractal dimension. In addition D is also a function of the fractal analysis method used and how the final fractal dimension is determined. To obtain a better overview of the effects of the steps involved in fractal analysis and the utility of this method, this chapter describes, using biological material from neuroscience, a non fractal based method, Sholl analysis and continues by discussing various processing options and the results obtained using fractal analysis. The effect of different fractal analysis methods, different computer applications of the same method, scale and resolution as well as regression analysis, which is for most methods the final step in determining D are discussed. This provides a platform for a better understanding of fractal analysis in research fields other than physics and mathematics and a more meaningful interpretation of results.