Orientation of particle attachment and local isotropy in diffusion limited aggregation (DLA)

We simulate 50 off-lattice DLA clusters, one million particles each. The probability distribution of the angle of attachment of arriving particles with respect to the local radial direction is obtained numerically. For increasing cluster size, $N$, the distribution crosses over extremely accurately to a cosine, whose amplitude decreases towards zero as a power-law in $N$. From this viewpoint, asymptotically large DLA clusters are locally $isotropic$. This contradicts previous conclusions drawn from density-density correlation measurements [P. Meakin, and T. Viscek, Phys. Rev. A {\bf 32}, 685 (1985)]. We present an intuitive phenomenological model random process for our numerical findings.