Diffusion-Limited Aggregation with a Restriction on the Growth Direction

A new type of two-dimensional diffusion-limited aggregation (DLA) is computer-simulated, in which the growth direction is restricted by the scale-invariant boundary. The seed particle from which the DLA cluster grows is located at the corner of a wedge-type boundary with the angle 90°. Two boundary conditions on the wedge are used; (a) absorption-type and (b) reflection-type. The average cluster length L along the bisector of the wedge and width W perpendicular to it are found to be scaled as L ∼ N ^{ν _//} and W ∼ N ^{∼ _⊥} for large N , where N is the total number of aggregated particles in the DLA cluster. It is also found that \(\nu_{//}{\cong}\nu_{\perp}\) even for the absorption-type boundary condition which yields anisotropic diffusion field, although the clusters are more elongated ( A ≡ L / W >1) than those for the reflection-type (\(A{\cong}1\)).