  In a recent paper (Bogoyavlenskiy V A 2002 \JPA \textbf{35} 2533), an
algorithm aiming to generate isotropic clusters of the on-lattice
diffusion-limited aggregation (DLA) model was proposed. The procedure consists
of aggregation probabilities proportional to the squared number of occupied
sites ($k^2$). In the present work, we analyzed this algorithm using the noise
reduced version of the DLA model and large scale simulations. In the noiseless
limit, instead of isotropic patterns, a $45^\circ$ ($30^\circ$) rotation in the
anisotropy directions of the clusters grown on square (triangular) lattices was
observed. A generalized algorithm, in which the aggregation probability is
proportional to $k^\nu$, was proposed. The exponent $\nu$ has a nonuniversal
critical value $\nu_c$, for which the patterns generated in the noiseless limit
exhibit the original (axial) anisotropy for $\nu<\nu_c$ and the rotated one
(diagonal) for $\nu>\nu_c$. The values $\nu_c = 1.395\pm0.005$ and $\nu_c =
0.82\pm 0.01$ were found for square and triangular lattices, respectively.
Moreover, large scale simulations show that there are a nontrivial relation
between noise reduction and anisotropy direction. The case $\nu=2$ (\bogo's
rule) is an example where the patterns exhibit the axial anisotropy for small
and the diagonal one for large noise reduction.
