Growth and form of zero-noise diffusion-limited-aggregation on the cubic lattice

The growth and form of zero-noise DLA clusters on a cubic lattice is investigated. Numerical simulations reveal a stable cluster consisting of six fourfold symmetric (almost planar) arms with a staircase structure along each arm. Empirical expressions are obtained for; the shape of the arms in the vicinity of the tips, the scaling of the arm lengths and the scaling of the tip growth rates. The empirical expressions are used to derive results for the growth rates along the arms of the cluster and for the step lengths in a needle staircase. These results are in good agreement with the numerical simulations.