We'll start with variations on 3 dimensions.

In two dimensions, go is commonly played on a 9x9, 13x13 or 19x19 board. It is possible to play on a 4x4 board, but that is not much of a game.

What is three-dimensional go? It is fairly easy to imagine a cube with a number of regular go boards stacked up on top of one another, with stones being placed on different boards and the whole game spanning all the boards at once. A stone on a board somewhere in the middle would have six liberties: the usual four on the same board, an adjacent point on the board directly above, and one on the next board directly below. Can you imagine trying to play such a game on a stack of 19 regular boards, each one the usual 19x19? Even if they were transparent glass instead of solid wood, it would be very unwieldy.

So let's scale it down. A lot. Imagine a stack of four boards, each 4x4, so we have a 4x4x4 game. It is feasible to construct such a board, and place regular black and white stones on it, and not too hard to see what is going on. A corner stone would have three liberties, an edge stone four, and a center stone six.

Would you like to play a game on such a board? Like right now? It's much easier than you might think to have such a board in front of you to play with. Rather than making one out of wood or cardboard or glass, we'll use a readily available free bit of software, Google's Sketch-Up. I just discovered it yesterday. It's rather neat. It's here: http://sketchup.google.com.

I made a 4x4x4 go "board" out of a matrix of light grey discs to represent the playing intersections. One places a stone by colouring in the appropriate disc. I coloured in red the top front left disc and in blue the bottom back right one. Here are some screenshots of the "board":




Here is a 3.5 MB animation of the board viewed from different angles. It is a regular avi file, exported from Sketch-Up, and should play on your regular media player. There's no sound, and it's not meant to be fancy at all. It's at http://www.yawnguy.com/go/sketch-up/4x4 ... tion-1.avi .

Note that the resolution of the video, and the resolution of images exported from it, suck. On the other hand, the screenshots from Sketch-Up itself are not bad at all.

Here is the 4x4x4 board you can play on: http://www.yawnguy.com/go/sketch-up/4x4x4_go_board.skp . It's an skp file, a Sketch-Up file. Open it in Sketch-Up, and you can rotate it around easily to view from any direction, pan, zoom in and out, etc.

The only tools you will need to use are:

1. Orbit tool (blue arrows with black tails curved around in a sphere) to rotate the "board" in three dimensions (it's intuitive, very easy to do).

2. Selection tool, the arrow right at the left of the menu bar. First use the orbit tool to rotate the board around until the disc you want to colour is isolated from adjacent stones as much as possible (most of them can be isolated in one go), then click on the select tool and select the disc by drawing a rectangle around it.

3. The paint bucket tool. Click on it, and a colour picker window will open up. You'll see a choice of materials, but ignore all that and find the colours in the materials selection box, then select what you want. The default colour of the discs is 000, if you screw up and need to start over. I suggest red and blue, or yellow and green, rather than black and white, but it's up to you, of course. Once you've selected the colour, hover the paint bucket cursor over the disc selected and click and it will start to colour. It might do it all in one go, or you might need to click a few times. It is possible you can't get all of it in one go, and you'll need to click on the orbit tool again and tweak the rotation of the board a bit, then have another go at the paint bucket.

Played strictly in three dimensions, is it a good game? Well, try it and see.

Alternatives to come soon.

Paul

I think a 7x7x7 board (= 343 intersections) might be better, as it is closest to the number of points we currently play on. Anyway, I have never played 3d go before, but I have a friend who has, and he reports that trying to make eyes or territory is much more difficult than in 2d.

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I can't remember where exactly I saw it, but I recall years ago coming across a 3D variant of go where it was set up like a Diamond crystal structure. The benefit was that even in 3D each stone would still have just 4 liberties (presumably) making capture/territory as easy as it was on a 2D goban. In practice of course, your own mileage my vary.

This is called Diamond Go, and is one of the more common 3d variants.

http://www.segerman.org/diamond/

There are a few freeware programs out there as well that allow you to play go on non standard boards, such as a cylinder rather than a square, etc etc.

That wire-frame diamond is beautiful! Thanks very much.

Paul

I've been trying to reinvent the wheel with one hand tied behind my back and my eyes closed. I should have looked around first.

There's a lovely little free program called FreedGo which takes up a whole 145 KB which enables playing 3D Go on a variety of boards.

You can even create your own custom boards using it.

Paul