Delesse principle and statistical fractal sets: 1. Dimensional equivalents

Dimensional equivalents of spatial objects and their projected images are w ell identified in stereology. However, at present, it is not clear if these and the Delesse and Rosiwal principles are applicable to fractal sets. Sca ling properties of statistically selfsimilar solid and pore sets of four so ils and sediments with contrasting genesis were described by the divider me thod. Two programs were used for the image analysis. Both programs are vari ants of the box-counting technique and are useful for the fractal analysis along the lines (Linfrac) and across the areas (Fractal). These programs we re tested using the images of ideal fractals and of some statistical fracta l sets. For all analysed images, the fractal dimension across an area was c lose to double the value of the set dimension along the Line. This relation was independent regarding the material nature, management system applied, horizon depth and profile localisation. Therefore, it seems to be necessary to correct the classical Delesse and Rosiwal principles for the statistica lly self-similar fractal sets. (C) 1998 Published by Elsevier Science B.V. All rights reserved.