Articles | Volume 15, issue 4
Nonlin. Processes Geophys., 15, 695–699, 2008
https://doi.org/10.5194/npg-15-695-2008
Nonlin. Processes Geophys., 15, 695–699, 2008
https://doi.org/10.5194/npg-15-695-2008

  26 Aug 2008

26 Aug 2008

Projection of compact fractal sets: application to diffusion-limited and cluster-cluster aggregates

F. Maggi F. Maggi
  • Berkeley Water Center, Civil and Environmental Engineering, 413 O'Brien Hall, University of California, Berkeley, CA 94720-1710, USA

Abstract. The need to assess the three-dimensional fractal dimension of fractal aggregates from the fractal dimension of two-dimensional projections is very frequent in geophysics, soil, and atmospheric sciences. However, a generally valid approach to relate the two- and three-dimensional fractal dimensions is missing, thus questioning the accuracy of the method used until now in practical applications. A mathematical approach developed for application to suspended aggregates made of cohesive sediment is investigated and applied here more generally to Diffusion-Limited Aggregates (DLA) and Cluster-Cluster Aggregates (CCA), showing higher accuracy in determining the three-dimensional fractal dimension compared to the method currently used.