Delesse principle and statistical fractal sets : 1. Dimensional equivalents

Dimensional equivalents of spatial objects and their projected images are well identified in stereology. However, at present, it is not clear if these and the Delesse and Rosiwal principles are applicable to fractal sets. Scaling properties of statistically self-similar solid and pore sets of four soils and sediments with contrasting genesis were described by the divider method. Two programs were used for the image analysis. Both programs are variants of the box-counting technique and are useful for the fractal analysis along the lines (Linfrac) and across the areas (Fractal). These programs were tested using the images of ideal fractals and of some statistical fractal sets. For all analysed images, the fractal dimension across an area was close 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 statistically self-similar fractal sets.

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