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Self‐Similitude and Fractal Dimension of Sand Grains
Author(s) -
Barak Phillip,
McSweeney Kevin,
Seybold Cathy A.
Publication year - 1996
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1996.03615995006000010013x
Subject(s) - fractal dimension , fractal dimension on networks , fractal , mathematics , geometry , box counting , fractal landscape , fractal derivative , fractal analysis , mathematical analysis
Fractal theory postulates that geological materials possess a noninteger, fractal dimension describing length‐surface‐volume relations and particle‐size distribution. We examined sand grains, composed largely of quartz, from several horizons of Wisconsin soils derived from glacial outwash for fractal dimension using image analysis of reflected light micrographs with NIH Image software. No evidence was found to support other than a Euclidean, i.e., regular dimension, relating the geometric properties of: (i) measured particle perimeter as a function of magnification 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.