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Matematicheskie Zametki, 2025, Volume 117, Issue 2, Pages 204–222
DOI: https://doi.org/10.4213/mzm14455 (Mi mzm14455) 		 
Peano curves and finite automata

A. V. Vlasov, S. B. Gashkov

Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm14455
Abstract: Finite automata implementing the Hilbert map from the unit interval to the unit square and its versions (a closed curve and a curve stationary almost everywhere) are constructed. Properties of this map, including special features of its restriction to rational numbers, are studied.
Keywords: Peano curve, Hilbert curve, finite automaton.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
The paper was published with the financial support of the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement 075-15-2022-284.
Received: 30.07.2024
Published: 13.05.2025
English version:
Mathematical Notes, 2025, Volume 117, Issue 2, Pages 214–228
DOI: https://doi.org/10.1134/S0001434625010213
Bibliographic databases:
Document Type: Article
UDC: 519.7+517.5
Language: Russian
Citation: A. V. Vlasov, S. B. Gashkov, “Peano curves and finite automata”, Mat. Zametki, 117:2 (2025), 204–222; Math. Notes, 117:2 (2025), 214–228
Citation in format AMSBIB
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\paper Peano curves and finite automata
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\pages 204--222
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\jour Math. Notes
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\vol 117
\issue 2
\pages 214--228
\crossref{https://doi.org/10.1134/S0001434625010213}
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