Kolam indiens, dessins sur le sable aux îles Vanuatu, courbe de Sierpinski et morphismes de monoïde

Allouche, Gabrielle; Allouche, Jean-Paul; Shallit, Jeffrey

Annales de l'Institut Fourier, Tome 56 (2006) no. 7, pp. 2115-2130.

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 $k\ge 1$.

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 $k\ge 1$.

Classification : 11B85, 68R15, 28A80, 01A07
Mot clés : kolam, dessins sur le sable, courbe de Sierpinski, morphismes de monoïde, suites automatiques
Keywords: kolam, drawings on the sand, Sierpinski curve, morphisms of monoid, automatic sequences

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