Anisotropic Diffusion Limited Aggregation: From Self-Similarity to Self-Affinity

Diffusion-limited particle aggregation is simulated with a modified growth rule. By means of a parameter the growth anisotropy along the axes of symmetry can be varied continually from isotropic to strongly anisotropic. For weak anisotropy one initially observes an isotropic structure with a fractal dimension D = 1.7 which crosses over to an anisotropic structure with two different scaling exponents D axial = 1.5 and D diagonal = 2.0 along the axes, respectively, along the diagonals, on a square lattice. One can understand the growth in the anisotropic regime in terms of classical aggregation, where the fluctuations are neglected.