Golden Ratio Nets and Sequences
| Autor: | Kirk, Nathan, Lemieux, Christiane, Wiart, Jaspar |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we introduce and study nets and sequences constructed in an irrational base, focusing on the case of a base given by the golden ratio $\phi$. We provide a complete framework to study equidistribution properties of nets in base $\phi$, which among other things requires the introduction of a new concept of prime elementary intervals which differ from the standard definition used for integer bases. We define the one-dimensional van der Corput sequence in base $\phi$ and two-dimensional Hammersley point sets in base $\phi$ and we prove some properties for $(0,1)-$sequences and $(0,m,2)-$nets in base $\phi$ respectively. We also include numerical studies of the discrepancy of point sets and sequences in base $\phi$ showing an improvement in distribution properties over traditional integer based Hammersley constructions. As motivation for future research, we show how the equidistribution notions that are introduced for base $\phi$ can be generalized to other irrational bases. Comment: 38 pages, 16 figures |
| Databáze: | arXiv |
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