Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown offlattice and clusters grown with antenna method with N f p = 3, 4, 5, 6, 7 and 8 allowed growth directions. With the help of variable probe particles technique we measure fractal dimension of such clusters D(N ) as a function of their size N . We propose that in the thermodynamic limit of infinite cluster size the aggregates grown with high degree of anisotropy (N f p = 3, 4, 5) tend to have fractal dimension D equal to 3/2, while off-lattice aggregates and aggregates with lower anisotropy (N f p > 6) have D ≈ 1.710. Noise-reduction procedure results in the change of universality class for DLA. For high enough noise-reduction value clusters with N f p ≥ 6 have fractal dimension going to 3/2 when N → ∞.

We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/R{dep}(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/R{dep}) function on an ensemble with 1000 clusters of 5×10{7} particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10 000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.

We test the multiscaling issue of diffusion-limited-aggregation (DLA) clusters using a modified algorithm. This algorithm eliminates killing the particles at the death circle. Instead, we return them to the birth circle at a random relative angle taken from the evaluated distribution. In addition, we use a two-level hierarchical memory model that allows using large steps in conjunction with an off-lattice realization of the model. Our algorithm still seems to stay in the framework of the original DLA model. We present an accurate estimate of the fractal dimensions based on the data for a hundred clusters with 50 million particles each. We find that multiscaling cannot be ruled out. We also find that the fractal dimension is a weak self-averaging quantity. In addition, the fractal dimension, if calculated using the harmonic measure, is a nonmonotonic function of the cluster radius. We argue that the controversies in the data interpretation can be due to the weak self-averaging and the influence of intrinsic noise.