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Locally catenative sequencesand Turtle graphics

Published online by Cambridge University Press:  22 August 2011

Juhani Karhumäki  and
Svetlana Puzynina
Juhani Karhumäki
Affiliation:
University of Turku, Department of Mathematics, 20014 Turku, Finland Turku Centre for Computer Science, 20014 Turku, Finland. karhumak@utu.fi
Svetlana Puzynina
Affiliation:
University of Turku, Department of Mathematics, 20014 Turku, Finland Turku Centre for Computer Science, 20014 Turku, Finland. karhumak@utu.fi Sobolev Institute of Mathematics, Novosibirsk 630090, Russia. svepuz@utu.fi
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Abstract

Motivated by striking properties of the well known Fibonacci wordwe consider pictures which are defined by this word and itsvariants via so-called turtle graphics. Such a picture can bebounded or unbounded. We characterize when the picture defined bynot only the Fibonacci recurrence, but also by a generalrecurrence formula, is bounded, the characterization beingcomputable.

Keywords

Combinatorics on wordslocally catenative sequencesturtle graphicsFibonacci word
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 45 , Issue 3 , July 2011 , pp. 311 - 330
Copyright
© EDP Sciences, 2011

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