On Horadam Sequences with Dense Orbits and Pseudo-Random Number Generators
Journal article
Authors | Bagdasar, O., Chen, M, Drăgan, V., Ivanov, I.G. and Popa, I.-L. |
---|---|
Abstract | Horadam sequence is a general recurrence of second order in the complex plane, depending on four complex parameters (two initial values and two recurrence coefficients). These sequences have been investigated over more than 60 years, but new properties and applications are still being discovered. Small parameter variations may dramatically impact the sequence orbits, generating numerous patterns: periodic, convergent, divergent, or dense within one dimensional curves. Here we explore Horadam sequences whose orbit is dense within a 2D region of the complex plane, while the complex argument is uniformly distributed in an interval. This enables the design of a pseudo-random number generator (PRNG) for the uniform distribution, for which we test periodicity, correlation, Monte Carlo estimation of π, and the NIST battery of tests. We then calculate the probability distribution of the radii of the sequence terms of Horadam sequences. Finally, we propose extensions of these results for generalized Horadam sequences of third order. |
Keywords | random numbers; geometric patterns; complex recurrent sequences; Horadam sequence; dense orbits |
Year | 2023 |
Journal | Mathematics |
Journal citation | 11 (5), pp. 1-16 |
Publisher | MDPI |
ISSN | 2227-7390 |
Digital Object Identifier (DOI) | https://doi.org/10.3390/math11051244 |
Web address (URL) | https://www.mdpi.com/2227-7390/11/5/1244 |
Accepted author manuscript | File Access Level Open |
Publisher's version | License File Access Level Open |
Output status | Published |
Publication dates | |
Online | 04 Mar 2023 |
Publication process dates | |
Accepted | 02 Mar 2023 |
Deposited | 26 Apr 2023 |
https://repository.derby.ac.uk/item/9xz90/on-horadam-sequences-with-dense-orbits-and-pseudo-random-number-generators
Download files
Accepted author manuscript
mathematics-11-01244-v2 (1).pdf | ||
File access level: Open |
Publisher's version
mathematics-11-01244-v2 (1).pdf | ||
License: CC BY 4.0 | ||
File access level: Open |
50
total views19
total downloads10
views this month0
downloads this month