SELF-SIMILITUDE AND FRACTAL DIMENSION OF SAND GRAINS

Fractal theory postulates that geological materials possess a noninteg er, fractal dimension describing length-surface-volume relations and p article-size distribution. We examined sand grains, composed largely o f quartz, from several horizons of Wisconsin soils derived from glacia l outwash for fractal dimension using image analysis of reflected ligh t micrographs with NIH Image software. No evidence was found to suppor t other than a Euclidean, i.e., regular dimension, relating the geomet ric properties of: (i) measured particle perimeter as a function of ma gnification or (ii) particle area and perimeter. In addition, particle -size distributions were better fit by lognormal distribution than by a fractal fragmentation dimension. Fractal theory would not appear to provide a useful description for these soil materials.