Fractal analysis of fracture patterns using the standard box-counting technique: valid and invalid methodologies



J. J. Walsh & J. Watterson

Abstract - On the basis of results of simple box-counting analysis, it has been suggested in several recent publications that natural fracture patterns are fractal. Fractal patterns are characterised by self-similarity of structure on a range of scales and provide straight line distributions on box-counting plots. New analysis of a fracture pattern that provided the most convincing straight-line box-counting curve previously published, shows that the curve is non-linear and, therefore, that the fracture pattern is not fractal. Non-linear box-counting curves are also characteristic of other natural fracture patterns analysed but spurious linear curves can be obtained if the area analysed extends beyond the mapped area.


Journal of Structural Geology 15, 1509-1512, 1993.