A cluster-cluster aggregation model with tunable fractal dimension

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Abstract
A hierarchical cluster-cluster aggregation computer model is introduced which allows one to build random fractal aggregates on a d-dimensional lattice with a fractal dimension fixed a priori. The algorithm works iteratively by sticking aggregates of the same number of particles at the correct centre-to-centre distance in order to recover the desired scaling. With the more efficient versions of the model, any fractal dimension ranging from 1 up to a d-dependent upper limit DM(d) can be obtained. One estimates DM(2) approximately=1.80+or-0.03 and DM(3) approximately=2.55+or-0.04. Calculations up to d=8 show that the ratio DM(d)/d decreases as d increases.