Noise-reduced diffusion-limited aggregation

A noise-reduced diffusion-limited-aggregation (DLA) model is explored on lattices with threefold, fourfold, and sixfold symmetry. In this model noise reduction on lattices with n-fold symmetry (n≤6) leads to clusters with n distinct arms whose structure is similar to very much larger DLA clusters grown without noise reduction. The structure of these clusters can be described in terms of the exponents ${\nu }_{?}$ and ${\nu }_{\perp }$ which describe how the length and width of the cluster arms grow with increasing cluster mass (M). Oscillation in the effective values of these exponents for large noise reduction factors makes it difficult to obtain the asymptotic (M→∞) value of ${\nu }_{?}$ and ${\nu }_{\perp }$. However, our results indicate that ${\nu }_{?}$ is close to (2/3 for n=3 but distinctly smaller than (2/3 for n=6. The results also indicate that ${\nu }_{?}$>${\nu }_{\perp }$ for n=3 but that ${\nu }_{?}$-${\nu }_{\perp }$≃0 for n=4 and 6. The simulation results are consistent with the idea that DLA clusters are fractals and for n≳4 they may be self-similar.