Sébastien Labbé

A Fibonacci Tile appearing in the fully packed loop diagram of the permutation \([16,15,13,12,19,22,9,23,26,8,6,29,30,5,31,32,1,2,28,3,4,27,25,7,10,24,11,14,21,20,18,17]\).

Done with Franco Saliola.

Le tournoi Chez Memphré 2010 est le centième tournoi d'ultimate auquel je participe.

• La liste de mes 100 premiers tournois
• Nombre de finales : 38.
• Nombre de tournois gagnés : 18.

A tamer wants to escape within a circle without being eaten by a lion who lives on the circle. The speed of the lion is 4 times that of the tamer. How can the tamer escape? There is a nice and clever solution in 2d, but does the naive solution where the tamer always moves oppositely to the lion works? In November 2009, a small script written in Sage by Xavier Provençal and Sébastien Labbé in Montpellier answers the question. To create the animation, download the script tamer.sage and run the commands:

sage: load tamer.sage
sage: l = range(0,1200,10)
sage: a = anime(l)
sage: a
Animation with 120 frames
sage: show(a)

How can the tamer escape? Can you find the solution?

The first 7 Fibonacci Tiles:

sage: path_op = dict(rgbcolor='red', thickness=1)
sage: fill_op = dict(rgbcolor='blue', alpha=0.3)
sage: options = dict(pathoptions=path_op, filloptions=fill_op, endarrow=False, startpoint=False)
sage: G = [words.fibonacci_tile(i).plot(**options) for i in range(7)]
sage: a = animate(G)
sage: a.show(delay=150)