Geodesic
Rotor-router aggregation on the layered square lattice
The electronic journal of combinatorics, Tome 17 (2010)
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In rotor-router aggregation on the square lattice $\mathbb{Z}^2$, 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.
DOI : 10.37236/424
Classification : 82B41, 82B20, 60G50
Mots-clés : router-router aggregation, random walks, growth model 
@article{10_37236_424,
     author = {Wouter Kager and Lionel Levine},
     title = {Rotor-router aggregation on the layered square lattice},
     journal = {The electronic journal of combinatorics},
     year = {2010},
     volume = {17},
     doi = {10.37236/424},
     zbl = {1203.82049},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/424/}
}
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%A Wouter Kager
%A Lionel Levine
%T Rotor-router aggregation on the layered square lattice
%J The electronic journal of combinatorics
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Wouter Kager; Lionel Levine. Rotor-router aggregation on the layered square lattice. The electronic journal of combinatorics, Tome 17 (2010). doi: 10.37236/424

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