Peano curves and finite automata

A. V. Vlasov, S. B. Gashkov

Lomonosov Moscow State University

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.

UDC: 519.7+517.5

Received: 30.07.2024

DOI: 10.4213/mzm14455

 English version: Mathematical Notes, 2025, 117:2, 214–228

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