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dc.contributor.authorBagdasar, Ovidiu
dc.contributor.authorLarcombe, Peter J.
dc.contributor.authorAnjum, Ashiq
dc.date.accessioned2016-11-16T13:28:37Z
dc.date.available2016-11-16T13:28:37Z
dc.date.issued2016-01-16
dc.identifier.citationBagdasar, O., Larcombe, P. J., Anjum, A. (2016) 'On the structure of periodic complex Horadam orbits', Carpathian Journal of Mathematics, 32 (1), pp. 29-36en
dc.identifier.issn1584-2851
dc.identifier.urihttp://hdl.handle.net/10545/620860
dc.description.abstractNumerous geometric patterns identified in nature, art or science can be generated from recurrent sequences, such as for example certain fractals or Fermat’s spiral. Fibonacci numbers in particular have been used to design search techniques, pseudo random-number generators and data structures. Complex Horadam sequences are a natural extension of Fibonacci sequence to complex numbers, involving four parameters (two initial values and two in the defining recursion), therefore successive sequence terms can be visualized in the complex plane. Here, a classification of the periodic orbits is proposed, based on divisibility relations between orders of generators (roots of the characteristic polynomial). Regular star polygons, bipartite graphs and multisymmetric patterns can be recovered for selected parameter values. Some applications are also suggested.
dc.language.isoenen
dc.publisherNorth University of Baia Mare (Romania)en
dc.relation.urlhttp://carpathian.ubm.ro/?m=past_issues&issueno=Vol.%2032%20(2016),%20No.%201en
dc.relation.urlhttp://carpathian.ubm.ro/?m=home/en
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.subjectDiscrete mathematicsen
dc.subjectApplied mathematicsen
dc.titleOn the structure of periodic complex Horadam orbitsen
dc.typeArticleen
dc.identifier.eissn1843-4401
dc.contributor.departmentUniversity of Derbyen
dc.identifier.journalCarpathian Journal of Mathematicsen
refterms.dateFOA2017-01-02T00:00:00Z
html.description.abstractNumerous geometric patterns identified in nature, art or science can be generated from recurrent sequences, such as for example certain fractals or Fermat’s spiral. Fibonacci numbers in particular have been used to design search techniques, pseudo random-number generators and data structures. Complex Horadam sequences are a natural extension of Fibonacci sequence to complex numbers, involving four parameters (two initial values and two in the defining recursion), therefore successive sequence terms can be visualized in the complex plane. Here, a classification of the periodic orbits is proposed, based on divisibility relations between orders of generators (roots of the characteristic polynomial). Regular star polygons, bipartite graphs and multisymmetric patterns can be recovered for selected parameter values. Some applications are also suggested.


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