  We explore the macroscopic consequences of lattice anisotropy for Diffusion
Limited Aggregation (DLA) in three dimensions. Simple cubic and BCC lattice
growths are shown to approach universal asymptotic states in a coherent
fashion, and the approach is accelerated by the use of noise reduction. These
states are strikingly anisotropic dendrites with a rich hierarchy of structure.
For growth on an FCC lattice, our data suggest at least two stable fixed points
of anisotropy, one matching the BCC case. Hexagonal growths, favouring six
planar and two polar directions, appear to approach a line of asymptotic states
with continuously tunable polar anisotropy. The more planar of these growths
visually resemble real snowflake morphologies.
  Our simulations use a new and dimension-independent implementation of the
Diffusion Limited Aggregation (DLA) model. The algorithm maintains a hierarchy
of sphere-coverings of the growth, supporting efficient random walks onto the
growth by spherical moves. Anisotropy was introduced by restricting growth to
certain preferred directions.
