Rotor-router aggregation on the layered square lattice

Details Rotor-router aggregation on the layered square lattice Rotor-router aggregation on the layered square lattice

2010-03-21

arxiv.org/abs/1003.4017v1

Elect. J. Combin. 17(1) #R152 (2010)

Mathematics

Combinatorics

11 pages, 3 figures.

Scientific paper

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.

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