Hdl Handle:
http://hdl.handle.net/10545/620860
Title:
On the structure of periodic complex Horadam orbits
Authors:
Bagdasar, Ovidiu ( 0000-0003-4193-9842 ) ; Larcombe, Peter J.; Anjum, Ashiq
Abstract:
Numerous 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.
Affiliation:
University of Derby
Citation:
Bagdasar, O., Larcombe, P. J., Anjum, A. (2016) 'On the structure of periodic complex Horadam orbits', Carpathian Journal of Mathematics, 32 (1), pp. 29-36
Publisher:
North University of Baia Mare (Romania)
Journal:
Carpathian Journal of Mathematics
Issue Date:
16-Jan-2016
URI:
http://hdl.handle.net/10545/620860
Additional Links:
http://carpathian.ubm.ro/?m=past_issues&issueno=Vol.%2032%20(2016),%20No.%201; http://carpathian.ubm.ro/?m=home/
Type:
Article
Language:
en
ISSN:
1584-2851
EISSN:
1843-4401
Appears in Collections:
Department of Electronics, Computing & Maths

Full metadata record

DC FieldValue Language
dc.contributor.authorBagdasar, Ovidiuen
dc.contributor.authorLarcombe, Peter J.en
dc.contributor.authorAnjum, Ashiqen
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.en
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
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