Systèmes de numération et fonctions fractales relatifs aux substitutions. (Numeration systems and fractal functions related to substitutions)

DOI10.1016/0304-3975(89)90041-8zbMath0679.10010OpenAlexW1991987591MaRDI QIDQ1124624

Publication date: 1989

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-3975(89)90041-8

zbMATH Keywords

fixed points numeration systems asymptotic formula finite alphabet substitution binary expansion sums of digits self-affine functions

Mathematics Subject Classification ID

Grammars and rewriting systems (68Q42) Radix representation; digital problems (11A63) Sequences and sets (11B99)

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Cites Work