Abnormal Stability in Growth of Diffusion-Limited Aggregation

Abstract

An abnormal and unsteady growth of an isotropic cluster in diffusion-limited aggregation (DLA) is observed in stability analyses. Macroscopic fluctuation due to the delay of transition from a dendritic tip to a tip-splitting growth induces the anisotropy of DLA. An asymptotic deformation factor ε_∞=0.0888 is obtained from large DLA clusters. A symmetric oval model proposed from the dual-stability growth of DLA gives an asymptotic fractal dimension of 1.7112 using ε_∞. The correspondence of this model to the box dimension is excellent.