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Persistent Patterns in Integer Discrete Circles

André Hoarau 1 Thierry Monteil 2
1 ECO - Exact Computing
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
2 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.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00799373
Contributor : Gwenaël Richomme <>
Submitted on : Tuesday, March 12, 2013 - 10:50:01 AM
Last modification on : Thursday, October 25, 2018 - 2:22:01 PM

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  • HAL Id : lirmm-00799373, version 1

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André Hoarau, Thierry Monteil. Persistent Patterns in Integer Discrete Circles. DGCI: Discrete Geometry for Computer Imagery, Mar 2013, Séville, Spain. pp.35-46. ⟨lirmm-00799373⟩

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