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arXiv · 1512.03909

A Contribution in the Rotor-router model

Hassan Douzi
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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.

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Hassan Douzi. 2015-12-12. A Contribution in the Rotor-router model. https://arxiv.org/abs/1512.03909

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