Deterministic screened growth models

Two deterministic modifications of the two dimensional screened growth models have been investigated. In one of these models (the threshold growth probability model) all of those sites with growth probabilities greater than ƒPmax are filled at each stage in the growth process. Here Pmax is the maximum growth probability for any of the unoccupied perimeter sites. This model leads to clusters with a power law relationship between the radius of gyration (Rg) and the cluster size M (Rg ≈ Mβ). For this model the effective fractal are changed dimensionally Dβ = 1/β varies continously as the parameters in the screening function are changed. In the second model (the continuous growth model) growth is assumed to occur in each of the unoccupied surface sites at a rate proportional to their growth probabilities. These sites become occupied when the growth in them reaches a fixed value of 1. This model leads to clusters with four dense symmetric arms. In this model the effective dimensionality Dβ crosses over from a value of 2.0 for small clusters or small length scales to a smaller value (probably 1.0) on longer length scales. Similar results were obtained from three dimensional models.