Rotor-router aggregation on the layered square lattice
Combinatorics
2011-09-28 v1
Abstract
In rotor-router aggregation on the square lattice Z^2, particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the cluster of occupied sites is a disk. We consider a small change to the routing mechanism for sites on the x- and y-axes, resulting in a limiting shape which is a diamond instead of a disk. We show that for a certain choice of initial rotors, the occupied cluster grows as a perfect diamond.
Keywords
Cite
@article{arxiv.1003.4017,
title = {Rotor-router aggregation on the layered square lattice},
author = {Wouter Kager and Lionel Levine},
journal= {arXiv preprint arXiv:1003.4017},
year = {2011}
}
Comments
11 pages, 3 figures.