Four dimensional chess?

My two-year Y!A anniversary, celebrated again with a new question: For a few months now I've been developing a chess variant which involves four spatial dimensions. I've finally gotten around to typing up a few notes on it and making a couple of diagrams if you're... show more My two-year Y!A anniversary, celebrated again with a new question:

For a few months now I've been developing a chess variant which involves four spatial dimensions. I've finally gotten around to typing up a few notes on it and making a couple of diagrams if you're interested:
http://my.ilstu.edu/~bmreini/Chess-basic...

My main question is, does the idea of 4D chess interest you? If so, then please have a read through the pdf. I've left quite a bit out really, particularly toward the end, so if you notice something interesting or have a comment, make a note of it here. [That's what my best answer criteria is for now.]

You'll notice I don't pick a solution for the slippery king; which one do you like? Do you have another suggestion? My main objective over the next few months is to decide on one central ruleset, which will be dubbed "TessChess" -- as in tesseract chess; "chesseract" is already taken by another supposedly 4D game -- and any other notable rules will be variants thereof in my mind.

Thanks!

[I've asked this in both the Mathematics section and the Board Games section, to get an impression on whether this is more a chess-players game or a mathematician's one.]
Update: sorry for the link, I guess it's too long for Y!A; it's
http://my.ilstu.edu/~bmreini/ Chess-basicmath.pdf
without the space in the URL.

and I do mean 4D, not 3D.
Update 2: For those who think this is impossible except by computer mediation, I should mention I had an almost weekly game last semester. I know that (particularly at first) it sounds absurd, but after one or perhaps two games you get a good intuition for the game. I've introduced it to several non-math/science people... show more For those who think this is impossible except by computer mediation, I should mention I had an almost weekly game last semester. I know that (particularly at first) it sounds absurd, but after one or perhaps two games you get a good intuition for the game. I've introduced it to several non-math/science people and they've grasped it fairly well.

I am working on a computer-based version of it though; I have a basic Java program from Sphinx chess, and plan on editing it into my rules, but am not presently well-versed in Java...

If you find yourself intrigued enough, and have someone else willing to play, there is a $4 solution: four chessboards from a dollar store, cut into quarters, and laid out as suggested in the pdf.

(And as I've realized it was me and not Y!A which broke the link, here's one which you can simply click, and not mess with pasting into your browser:
http://my.ilstu.edu/~bmreini/Chess-basic...
)
Update 3: I thought you might notice that I didn't mention anything about the original setup. In particular, bishops all are stuck on one color, which seems unsavory. We're still playing around with different setups, but this one has a very good level of mutual protection among the pieces. Also, I've... show more I thought you might notice that I didn't mention anything about the original setup. In particular, bishops all are stuck on one color, which seems unsavory. We're still playing around with different setups, but this one has a very good level of mutual protection among the pieces.

Also, I've recently realized that a king+queen can checkmate a lone king. Not quite as good as a king+rook being able to do it, but it makes it a bit nicer than it first appears to have a king with up to 80 moves.

As I make updates to the paper(s) they'll make their way to that link, at least until my university site is shut down.
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