Universal behavior of the shortest-path aggregation

The shortest-path aggregation in a two-dimensional square lattice is studied numerically. We find universal behavior of the cluster formation when the released particles are weakly correlated, and a distinct universal behavior for clusters generated by a strongly correlated release. In particular, we find the fractal dimension {ital D}=1.20{plus minus}0.01 when the released particles are weakly correlated, while a one-dimensional object is obtained when the correlation is strong. We also find the anisotropic exponent {delta}=1.0 in the weak-correlation region.