Practical application of fractal analysis: Problems and solutions

Fractal analysis is now common in many disciplines, but its actual application is often affected by methodological errors which can bias the results. These problems are commonly associated with the evaluation of the fractal dimension D and the range of scale invariance R. We show that by applying the most common algorithms for fractal analysis (Walker's Ruler and box counting), it is always possible to obtain a fractal dimension, but this value might be physically meaningless. The chief problem is the number of data points, which is bound to be insufficient when the algorithms are implemented by hand. Further, erroneous application of regression analysis can also lead to incorrect results. To remedy the former point, we have implemented a convenient numerical program for box counting. After discussing the rationale of linear regression and its application to fractal analysis, we present a methodology that can be followed to obtain meaningful results.