Cluster-particle aggregation with fractal (Levy flight) particle trajectories

The effects of particle trajectories on the structure of aggregates formed by cluster-particle aggregation have been explored by computer simulation. With the use of Levy-flight particle trajectories, clusters with a continuous range of effective dimensionalities between the limits of the Witten-Sander ($D\simeq \frac{5}{3}$ for $d=2\mathrm{}$) and Vold-Sutherland models ($D\simeq 2.0$ for $d=2\mathrm{}$) can be generated. The effective dimensionality varies continuously with the exponent which describes the distribution of step lengths in the Levy-flight trajectory, but there does not seen to be a unique (1:1) relationship between the dimensionality of the trajectory and the dimensionality of the cluster.