Multiscaling in diffusion-limited aggregation

It is shown using large-scale simulations that the density profile in diffusion-limited aggregation in two dimensions satisfies a scaling form (multiscaling) of the type g(r,R)=${\mathit{r}}^{\mathrm{-}\mathit{d}+\mathit{D}(\mathit{r}/\mathit{R})}$C(r/R), where r is the distance from the origin, R is the radius of gyration, and C(x) is an amplitude. Contrary to standard scaling, which predicts D(x)=const, here D(x) is found to depend continuously on x.