Life In 19x19

There was a thread a while back about alternative tilings for go (viewtopic.php?f=45&t=1163&hilit=hexagon&start=20).

I was thinking about this again, and I like the trihexagonal tiling:


Can you spot the snapback?

This has the nice property that each point has 4 liberties, and it's uniform. Also it seems like 6 stones make life in the corner:

I had to convince myself that your trihexagonal go board is not equivalent the our normal square go board. But of course it isn't. In normal go two neighbouring points don't share a common neighbour in trihexagonal go they do. I like your idea!

Interesting. When are we going to see first trihexagonalevich?

a bit off topic but i worked on this lattice (called the kagome lattice -from a japanese name for basket or something) during my physics day and the geometric properties are crazy ,and as a result the physics properties of the heisenberg model on it are crazy too (the ground state might have residual entropy at T=0 because it remains ennormously degenerated ). it would be very very different from a square lattice even if coordinance is 4 too: for example it is not bipartite ie you cannot divide it into 2 sublattices where no 2 summit on the same sublattice are niegihbors (this is trivial with a square lattice )

in some sense you always have bad shape: a 2 stone chain have only 5 lib instead of 6 in the square lattices. an empty triangle have 7 libs on the square, but a "full triangle" (3 stones of same color on same triangle) have 5 on the kagome.

making eyes in the center would be near impossible: you need at least 9 stones to enclose a single eye and be connected (vs 7 on the square lattice) and 12 stones to be alive in the center

on the other hand seki might be easier to get

tj86430 wrote:Interesting. When are we going to see first trihexagonalevich?

I'd like to try it, but I'm not sure if there's an easy way to do the diagrams. For these I'm adding the stones manually in inkscape (svg editor). It's not too difficult, but it does require editing in another program.

perceval wrote:making eyes in the center would be near impossible: you need at least 9 stones to enclose a single eye and be connected (vs 7 on the square lattice) and 12 stones to be alive in the center

What about this shape?

And you only need 4 stone to be alive in the acute corner (the straight line is enough) : it's a cute corner

In Esmeraldons first diagram can black connect his left group to his lower right group? I believe he can not.

How does that work Tryss? I can't see it.

hyperpape wrote:How does that work Tryss? I can't see it.

The second points from the corner are miai.

hyperpape wrote:How does that work Tryss? I can't see it.

The two "1-2" points are miai for separating the corner space
into two eyes. So it's not Benson alive, but alive it is.

-John

Arguably, I would guess any single stone on an otherwise empty board is "alive" by that measure

I don't want to spoil the fun, but this idea has been implemented long ago in Medusa.
You can find the game at [sl=Medusa]Sensei's[/sl] and it is also featured in R. Wayne Schmittberger's 'New Rules for Classic Games' (John Wiley & Sons, Inc. New York; ISBN 0-471-53621-0).

I don't know how to render it, but a spherical trihexagoal board would be pretty cool.

christian freeling wrote:I don't want to spoil the fun, but this idea has been implemented long ago in Medusa.
You can find the game at [sl=Medusa]Sensei's[/sl] and it is also featured in R. Wayne Schmittberger's 'New Rules for Classic Games' (John Wiley & Sons, Inc. New York; ISBN 0-471-53621-0).

Playing go on other graphs is such a obvious idea that I believe any claims of anteriority are pretty pointless.

HermanHiddema wrote:Playing go on other graphs is such a obvious idea that I believe any claims of anteriority are pretty pointless.

I hope factual information bearing on the subject isn't. Medusa isn't 'Go on another graph' either but a fairly exotic variant quietly orbiting the outer fringes of the Golar system. Before anyone accuses me of claiming it's a big deal, we never even made an applet for it at mindsports.