Is DLA Locally Isotropic or Self-Affine?

TL;DR

This paper uses simulations to demonstrate that DLA clusters are not self-affine, showing that the asymmetry of the last step diminishes algebraically with deposit thickness, challenging previous claims.

Contribution

The study provides the first clear evidence that DLA clusters are not self-affine by analyzing the asymmetry of the last step before sticking.

Findings

Asymmetry tends to zero algebraically with deposit thickness

DLA clusters are not self-affine, contrary to previous claims

Simulation results clarify the nature of DLA cluster morphology

Abstract

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.