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Motivated by striking properties of the well known Fibonacci word we consider pictures which are defined by this word and its variants via so-called turtle graphics. Such a picture can be bounded or unbounded. We characterize when the picture defined by not only the Fibonacci recurrence, but also by a general recurrence formula, is bounded, the characterization being computable.
@article{ITA_2011__45_3_311_0,
author = {Karhum\"aki, Juhani and Puzynina, Svetlana},
title = {Locally catenative sequences and {Turtle} graphics},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {311--330},
publisher = {EDP-Sciences},
volume = {45},
number = {3},
year = {2011},
doi = {10.1051/ita/2011104},
mrnumber = {2836492},
zbl = {1228.68042},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita/2011104/}
}
TY - JOUR AU - Karhumäki, Juhani AU - Puzynina, Svetlana TI - Locally catenative sequences and Turtle graphics JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2011 SP - 311 EP - 330 VL - 45 IS - 3 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita/2011104/ DO - 10.1051/ita/2011104 LA - en ID - ITA_2011__45_3_311_0 ER -
%0 Journal Article %A Karhumäki, Juhani %A Puzynina, Svetlana %T Locally catenative sequences and Turtle graphics %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2011 %P 311-330 %V 45 %N 3 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita/2011104/ %R 10.1051/ita/2011104 %G en %F ITA_2011__45_3_311_0
Karhumäki, Juhani; Puzynina, Svetlana. Locally catenative sequences and Turtle graphics. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 45 (2011) no. 3, pp. 311-330. doi: 10.1051/ita/2011104
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