Multifractal Geometry of Diffusion-Limited Aggregates

Abstract
Off-lattice diffusion-limited aggregation (DLA) clusters are shown to have multifractal geometry. We determine the Dq spectrum associated with the mass distribution using an improved sand box technique and demonstrate that they decrease monotonically with increasing q. From our results it follows that the commonly used methods for the determination of the fractal dimension of DLA clusters yield Dq=2 which is smaller than the true fractal dimension Dq=0.