Open AccessPractical application of fractal analysis: problems and solutions
Author(s) -
Gonzato Guido,
Mulargia Francesco,
Marzocchi Warner
Publication year - 1998
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1046/j.1365-246x.1998.00461.x
Subject(s) - fractal analysis , fractal , box counting , fractal dimension , computer science , dimension (graph theory) , fractal dimension on networks , algorithm , fractal landscape , range (aeronautics) , point (geometry) , mathematics , scale (ratio) , statistics , geometry , mathematical analysis , combinatorics , physics , materials science , quantum mechanics , composite material
Summary 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 χef 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 νmerical 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.