On the structure of periodic complex horadam orbits
Journal article
Bagdasar, O.D., Larcombe, P.J., Anjum, A. and Bagdasar, O. 2016. On the structure of periodic complex horadam orbits. Carpathian Journal of Mathematics.
| Authors | Bagdasar, O.D., Larcombe, P.J., Anjum, A. and Bagdasar, O. |
|---|---|
| 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. |
Numerous geometric patterns identified in nature, art or science can be generated from recurrent | |
| Keywords | Discrete mathematics; Applied mathematics |
| Year | 2016 |
| Journal | Carpathian Journal of Mathematics |
| Publisher | North University of Baia Mare (Romania) |
| ISSN | 1584-2851 |
| 1843-4401 | |
| Web address (URL) | http://www.scopus.com/inward/record.url?eid=2-s2.0-84986882860&partnerID=MN8TOARS |
| Publication dates | 2016 |
| Publication process dates | |
| Deposited | 16 Nov 2016, 13:28 |
| Contributors | University of Derby |
| File | File Access Level Open |
| File | File Access Level Open |
| File |
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