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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:
IDs | Image | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
S, H, W, |
|
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)