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Talk:Meanders

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What to think of the following correspondence?

Here is an example of a meander on a 5-by-3 grid:

A meander on a (5,3)-grid
IDs Image

S, H, W,
E, W, V,
S, A, N,
V, E, W,
E, H, N,

(2 orientations)

Meander BR.png Meander LR.png Meander LB.png
Meander TR.png Meander LB.png Meander BT.png
Meander BR.png Meander LT & BR.png Meander LT.png
Meander BT.png Meander TR.png Meander LB.png
Meander TR.png Meander LR.png Meander LT.png

and the corresponding lattice graph (where a blue edge corresponds to an edge crossed by a meander) (unfortunately the correspondence is not one-to-one, since from the lattice graph we cannot determine which of the two possible choices applies for the central tile of the non self-crossing meander)








 
 
 






 
 
 






 
 
 






 
 
 






 
 
 






A kludge to get a one-to-one correspondence would be to add a diagonal edge (bottom left to top right) in the center, with the proviso that a meander cannot cross it.

Daniel Forgues 07:51, 2 January 2012 (UTC)