Practical application of fractal analysis: Problems and solutions: Geophys

Fractal analysis is now common in many disciplines, but its actual application is often a¡ected by methodological errors which can bias the results. These problems are com-monly 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 insu¤cient 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. Key word: fractals.