Method for computing the three-dimensional capacity dimension from two-dimensional projections of fractal aggregates

The current theory of projections of fractals is considered in this paper with application to fractal aggregates. In particular, this theory does not accurately enable the computation of the capacity dimension of three-dimensional aggregates from the capacity dimension of their two-dimensional projections. Herein we propose to compute the three-dimensional capacity dimension from the perimeter-based fractal dimension, using a semiempirical equation, an approach not applied earlier.