NUMERICAL INVESTIGATION OF 2-DIMENSIONAL PROJECTIONS OF RANDOM FRACTAL AGGREGATES

Three-dimensional random fractal aggregates of variable fractal dimension D ranging from 1 to 2.5 are built on a cubic lattice using a hierarchical computer algorithm. The fractal dimensions of the surface Ds and the perimeter Dp of their two-dimensional projections have been computed. From an extrapolation of finite size results for aggregates containing up to 8192 particles, it is found that Ds and Dp are both equal to D for D<2 while Ds=2 for D>2. The numerical results are consistent with a nontrivial value of Dp, varying continuously with D, for D>2. © 1994 The American Physical Society.