Indian kolam, drawings on the sand in the Vanuatu Islands, Sierpinski curve, and morphisms of monoids

Gabrielle Allouche[1]; Jean-Paul Allouche[2]; Jeffrey Shallit[3]

  • [1] 24 rue Marceau 37000 Tours (France)
  • [2] CNRS, LRI, Bâtiment 490 91405 Orsay Cedex (France)
  • [3] University of Waterloo School of Computer Science Waterloo, Ontario N2L 3G1 (Canada)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 7, page 2115-2130
  • ISSN: 0373-0956

Abstract

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We prove that the drawing of a classical Indian kolam (which one also finds in the tradition of drawings on the sand in the Vanuatu islands) can be described by a morphism of monoids. The corresponding infinite sequence is related to the celebrated Prouhet-Thue-Morse sequence, but it is not k -automatic for any integer k 1 .

How to cite

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Allouche, Gabrielle, Allouche, Jean-Paul, and Shallit, Jeffrey. "Kolam indiens, dessins sur le sable aux îles Vanuatu, courbe de Sierpinski et morphismes de monoïde." Annales de l’institut Fourier 56.7 (2006): 2115-2130. <http://eudml.org/doc/10199>.

@article{Allouche2006,
abstract = {Nous montrons que le tracé d’un kolam indien classique, que l’on retrouve aussi dans la tradition des dessins sur le sable aux îles Vanuatu, peut être engendré par un morphisme de monoïde. La suite infinie morphique ainsi obtenue est reliée à la célèbre suite de Prouhet-Thue-Morse, mais elle n’est $k$-automatique pour aucun entier $k \ge 1$.},
affiliation = {24 rue Marceau 37000 Tours (France); CNRS, LRI, Bâtiment 490 91405 Orsay Cedex (France); University of Waterloo School of Computer Science Waterloo, Ontario N2L 3G1 (Canada)},
author = {Allouche, Gabrielle, Allouche, Jean-Paul, Shallit, Jeffrey},
journal = {Annales de l’institut Fourier},
keywords = {kolam; drawings on the sand; Sierpinski curve; morphisms of monoid; automatic sequences},
language = {fre},
number = {7},
pages = {2115-2130},
publisher = {Association des Annales de l’institut Fourier},
title = {Kolam indiens, dessins sur le sable aux îles Vanuatu, courbe de Sierpinski et morphismes de monoïde},
url = {http://eudml.org/doc/10199},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Allouche, Gabrielle
AU - Allouche, Jean-Paul
AU - Shallit, Jeffrey
TI - Kolam indiens, dessins sur le sable aux îles Vanuatu, courbe de Sierpinski et morphismes de monoïde
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 7
SP - 2115
EP - 2130
AB - Nous montrons que le tracé d’un kolam indien classique, que l’on retrouve aussi dans la tradition des dessins sur le sable aux îles Vanuatu, peut être engendré par un morphisme de monoïde. La suite infinie morphique ainsi obtenue est reliée à la célèbre suite de Prouhet-Thue-Morse, mais elle n’est $k$-automatique pour aucun entier $k \ge 1$.
LA - fre
KW - kolam; drawings on the sand; Sierpinski curve; morphisms of monoid; automatic sequences
UR - http://eudml.org/doc/10199
ER -

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