Multifractal scaling of 3D diffusion-limited aggregation

We study the multifractal (MF) properties of the set of growth probabilities {pi} for 3D off-lattice diffusion-limited aggregation (DLA). We find that: (i) the {pi} display MF scaling for all moments-in contrast to 2D DLA, where one observes a “phase transition” in the MF spectrum for negative moments; (ii) multifractality is also displayed by the pi located in a shell of reduced radius x ≡ rRg, where Rg is the radius of gyration of the cluster and r the radius of the shell; (iii) the average value αav of α ≡ -In p/InM in a shell of reduced radius x in a cluster of mass M is a function that does not depend on the cluster mass but only on x.