Is DLA Locally Isotropic or Self-Affine?
  We present results of simulations which show unambiguously that DLA clusters are not self-affine, in contrast to frequent claims. The measured observable is the asymmetry of the last step of a walker before he sticks to the growing cluster. Using deposition onto an originally straight line off lattice, we show that this asymmetry tends to zero algebraically with the thickness of the deposit. 
Rainer Hegger and Peter Grassberger