A Contribution in the Rotor-router model
Abstract
In this paper I propose to approach the Rotor-router problem by considering it as one example of a big family of many other similar models. The study of some specific samples of them may contribute, in my opinion, at a more understanding of the J.Propp model. In fact we can easily generalize the Rotor-router to many other models, with different regular geometric shapes, by slightly changing the ants' displacements rules. The two directions Rotor-Router (RR2) is particularly interesting because in it's Abelian version it is generated by an easy mathematical explicit scheme. Moreover we can also generate the J.Propp Rotor-Router using a similar iterative explicit algorithm. The study of RR2 establishes also a relationship between the J.Propp model and a family of symmetrical models which generates the same round forms.
Cite
@article{arxiv.1512.03909,
title = {A Contribution in the Rotor-router model},
author = {Hassan Douzi},
journal= {arXiv preprint arXiv:1512.03909},
year = {2015}
}