Persistent Patterns in Integer Discrete Circles

André Hoarau 1 Thierry Monteil 1
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We study patterns that appear in discrete circles with integer center and radius. As the radius goes to infinity, the patterns get closer to digital straight segments: the notion of tangent words (described in Monteil DGCI 2011) allows to grasp their shape. Unexpectedly, some tangent convex words do not appear infinitely often due to deep arithmetical reasons related to an underlying Pell-Fermat equation. The aim of this paper is to provide a complete characterization of the patterns that appear in integer discrete circles for infinitely many radii.
Type de document :
Communication dans un congrès
DGCI'2013: 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Mar 2013, Séville, Spain. 7749, pp.35-46, 2013, Lecture Notes in Computer Science. 〈http://dgci2013.us.es/〉
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00799373
Contributeur : Gwenaël Richomme <>
Soumis le : mardi 12 mars 2013 - 10:50:01
Dernière modification le : jeudi 11 janvier 2018 - 06:26:07

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André Hoarau, Thierry Monteil. Persistent Patterns in Integer Discrete Circles. DGCI'2013: 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Mar 2013, Séville, Spain. 7749, pp.35-46, 2013, Lecture Notes in Computer Science. 〈http://dgci2013.us.es/〉. 〈lirmm-00799373〉

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