K. E. Bauman, “The dilation factor of the Peano–Hilbert curve”, Mat. Zametki, 80:5 (2006), 643–656; Math. Notes, 80:5 (2006), 609

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Matematicheskie Zametki, 2006, Volume 80, Issue 5, Pages 643–656
DOI: https://doi.org/10.4213/mzm3074 (Mi mzm3074)

This article is cited in 38 scientific papers (total in 38 papers)

The dilation factor of the Peano–Hilbert curve

K. E. Bauman

M. V. Lomonosov Moscow State University

Full-text PDF (479 kB) Citations (38)

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DOI: https://doi.org/10.4213/mzm3074

Abstract: It is proved that the maximum value of the ratio

| p (x) - p (y) |^{2} / | x - y |

$|p(x)-p(y)|^2/|x-y|$ for the Peano–Hilbert curve

p : [0, 1] = I \to I^{2}

$p\colon[0,1]=I\to I^2$ is equal to 6.

Received: 03.04.2006

English version:
Mathematical Notes, 2006, Volume 80, Issue 5, Pages 609–620
DOI: https://doi.org/10.1007/s11006-006-0182-8

Bibliographic databases:

UDC: 514.8

Language: Russian

Citation: K. E. Bauman, “The dilation factor of the Peano–Hilbert curve”, Mat. Zametki, 80:5 (2006), 643–656; Math. Notes, 80:5 (2006), 609–620

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm3074

https://doi.org/10.4213/mzm3074

https://www.mathnet.ru/eng/mzm/v80/i5/p643

This publication is cited in the following 38 articles:

A. V. Vlasov, S. B. Gashkov, “Krivye Peano i konechnye avtomaty”, Matem. zametki, 117:2 (2025), 204–222
Huihui Xu, Yijun Yang, Angelica I. Aviles-Rivero, Guang Yang, Jing Qin, Lei Zhu, Lecture Notes in Computer Science, 15004, Medical Image Computing and Computer Assisted Intervention – MICCAI 2024, 2024, 667
Hongtao Wu, Yijun Yang, Huihui Xu, Weiming Wang, Jinni Zhou, Lei Zhu, Proceedings of the 32nd ACM International Conference on Multimedia, 2024, 7881
P. A. Borodin, K. S. Shklyaev, “Density of quantized approximations”, Russian Math. Surveys, 78:5 (2023), 797–851
Yuri Malykhin, Evgeny Shchepin, “Search of fractal space-filling curves with minimal dilation”, Discrete Comput. Geom., 70 (2023), 189–213
Julián Patiño Ortiz, Miguel Patiño Ortiz, Miguel-Ángel Martínez-Cruz, Alexander S. Balankin, “A Brief Survey of Paradigmatic Fractals from a Topological Perspective”, Fractal Fract, 7:8 (2023), 597 $https://doi.org/10.3390/fractalfract7080597$
Wanli Chen, Xinge Zhu, Guojin Chen, Bei Yu, Lecture Notes in Computer Science, 13662, Computer Vision – ECCV 2022, 2022, 730
H. K. Dai, H. C. Su, “Studies of Norm-Based Locality Measures of Two-Dimensional Hilbert Curves”, SN COMPUT. SCI., 2:5 (2021)
Yu. V. Malykhin, E. V. Shchepin, “Minimal self-similar Peano curve of genus 5 $\times$ 5”, Dokl. Math., 101:2 (2020), 135–138
H. K. Dai, H. C. Su, Lecture Notes in Computer Science, 12466, Future Data and Security Engineering, 2020, 169
Samia Bentaieb, Abdelaziz Ouamri, Mokhtar Keche, 2019 6th International Conference on Image and Signal Processing and their Applications (ISPA), 2019, 1
A.A. Mikhaylov, Alatar Ali Ikhsan, 2019 International Multi-Conference on Industrial Engineering and Modern Technologies (FarEastCon), 2019, 1
Anant A. Joshi, Maulik C. Bhatt, Arpita Sinha, 2019 Sixth Indian Control Conference (ICC), 2019, 338
Galantai A., “Always Convergent Methods For Nonlinear Equations of Several Variables”, Numer. Algorithms, 78:2 (2018), 625–641
Estevez-Rams E., Estevez-Moya D., Martinez-Camejo Y., Gomez-Gomez D., Aragon-Fernandez B., “Hilbert Curves in Two Dimensions”, Rev. Cub. Fis., 34:1 (2017), 9–18
Dai H.K., Su H.C., “Norm-Based Locality Measures of Two-Dimensional Hilbert Curves”, Algorithmic Aspects in Information and Management, Lecture Notes in Computer Science, 9778, eds. Dondi R., Fertin G., Mauri G., Springer Int Publishing Ag, 2016, 14–25
Estevez-Rams E., Perez-Demydenko C., Aragon Fernandez B., Lora-Serrano R., “Visualizing Long Vectors of Measurements By Use of the Hilbert Curve”, Comput. Phys. Commun., 197 (2015), 118–127
Perez-Demydenko C., Brito-Reyes I., Aragon Fernandez B., Estevez-Rams E., “The Complete Set of Homogeneous Hilbert Curves in Two Dimensions”, Appl. Math. Comput., 234 (2014), 531–542
K. E. Bauman, “Lower estimate of the square-to-linear ratio for regular Peano curves”, Discrete Math. Appl., 24:3 (2014), 123–128
Michael Bader, Texts in Computational Science and Engineering, 9, Space-Filling Curves, 2013, 15

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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