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4*Chess (four dimensional chess). Four dimensional chess using sixteen 4x4 boards & 96 pieces. (4x4x16, Cells: 256) [All Comments] [Add Comment or Rating]
Fergus Duniho wrote on 2015-12-20 UTC
The Diagram Designer is limited to 2D graphics, and it uses a 2D coordinate system. To represent a 4D game, you have to figure out how to represent it within those limitations. A 3D or 4D board would be composed of separate 2D boards, and you could use hyphens to remove spaces to separate different 2D boards from each other. Here's <A HREF="">an example</A> of how a 4D game could be done. A piece can move up or down by moving to a space on a board above or below it, and it can travel through the 4th dimension by moving to a board on the left or right. The tricky part is coming up with a 4D coordinate system. Since it has to be done with a 2D coordinate system, each of the first two dimensions has to be paired with one of the latter two. So you can't simply write coordinates in the order of first dimension, second dimension, third dimension, fourth dimension. I did it in the order of fourth dimension, files, ranks, third dimension. However I did it, I wanted to keep files and ranks together in the usual order. So they appear in the middle. The fourth dimension is paired with files, because both are spaced to the left and right of each other, and I paired the third dimension with ranks, because both are spaced above and below each other. Although I could use capital letters and lowercase letters for different dimensions, there wasn't another number system to use in place of Arabic numerals. So I had to use Arabic numerals twice, and I didn't want the two coordinates using Arabic numerals to touch. So I used Arabic numerals for the fourth dimension, which is on the left next to files, and I used capital letters for the third dimension, which is on the right next to ranks.

Kevin Pacey wrote on 2015-12-20 UTC
A question for Fergus (or possibly Ben). Offhand can you tell me if there is any hopefully straightforward way the Chess Variants Page's Diagram Designer can generate a diagram for a (4x4x4x4) 4-dimensional 4*Chess position? I haven't been able to tell for certain from what little I've read of the Game Courier documentation, though I get the impression creating such a diagram this way may not be simple to know how to do. 

I'm thinking of this as a possible project that I'm not in a hurry to start or finish, but I would like to know how to make such a diagram if I wish to. No hurry for me, that is, since there are about 20 positions I've used crude diagrams for in my 4*Chess webpage submission.

Fwiw Ben's variant 'Tess Chess' webpage shows a 4x4x4x4 4-dimensional variant diagram of his, although the checker pattern for the boards alternates its colours in a different way than it does for my 4*Chess variant:

Kevin Pacey wrote on 2015-11-14 UTC
By editing, I've added descriptions of the ideas of Crazyhouse & Bughouse versions of 4*Chess (namely 4*Crazyhouse & 4*Bughouse) to the 'Notes' section of my submission above.

Kevin Pacey wrote on 2015-11-07 UTC
Thought I'd mention that 4*Chess got its rules for 4*Chess Pawn movements (& its last rank promotion rule applying only to the appropriate corner mini-board) partly because of the starting position for it, which was designed to allow any square in 4*Chess to be reached by exactly one of the eight 4*Chess Balloons (aka Dirigibles) one starts a game with. For that to happen, essentially all mini-boards of a single quadrant of four mini-boards had to have two opposite coloured 4*Chess Balloons on the same rank of each mini-board involved, as is the case for both sides in the setup position. That meant that for both sides some pawns were going to be closer to promoting from the setup position than others, even if I chose to allow promotions to occur on the last rank of all 4 mini-boards that were on a player's last row of mini-boards. On top of that, from the start I wished promotions only to occur in a corner quadrant where the enemy 4*Chess King starts the game, and so I was happy enough to make that choice instead.

For anyone who missed it, I made edits to my previous comment.

Kevin Pacey wrote on 2015-11-05 UTC
I've now put the diagram back in, with the White 4*Chess R added, as you suggested Ben. I've also added a total of 11 new diagrams illustrating other mates with various piece combinations. In addition, I've added two more White 4*Chess pawns to the diagram that illustrated possible legal pawn moves, putting the two 4*Chess Pawns in opposite corner mini-boards to hopefully help to clarify how pawns move even further.

Kevin Pacey wrote on 2015-11-05 UTC
Sorry I already deleted the diagram in question, as my sole idea was to try to show a 'basic' mate with just two 4*Chess Unicorns, which unfortunately now seems an impossible task.

Ben Reiniger wrote on 2015-11-05 UTC
I would leave it in, but add a rook to, say, 4134.

I had realized that a K+Q wins against bare k, but hadn't bothered to put much thought into other mates (even non-forcible ones) before.  I think these are quite interesting.

Kevin Pacey wrote on 2015-11-05 UTC
You are right Ben that the Black 4*Chess K is not mated (i.e. can escape) in the diagram I made of White having two 4*Chess Unicorns (& his 4*Chess K) vs. a lone Black 4*Chess K (it seems there can be no similar position constructed where there is a mate on the board with this material balance). I'll go back and delete the diagram in question from my submission.

Ben Reiniger wrote on 2015-11-05 UTC
Thanks for the additional diagrams.  The pawns then have essentially three "forward" directions and one lateral, and you do allow a capturing move that is "forward" in two directions.  It's maybe interesting then that pawns start at different distances to their promotion zone, but they can speed ahead sometimes with capture.

I'll look more carefully later, but in your first checkmate diagram, can't the king escape to 4334 or 4434?

Kevin Pacey wrote on 2015-11-01 UTC
I've edited a couple of my comments & original submission for 4*Chess, in case anyone hasn't noticed.

Kevin Pacey wrote on 2015-10-31 UTC
Regarding the name "Unicorn", I originally preferred to use it in my 4D variant (rather than "Nun", or any other name), until I saw the wiki link on fairy chess pieces, which didn't appear to me to include the way I was using "Unicorn". Apparently I looked in haste, because it now appears to me that it does. I'll go back and edit my submission to change the name "Nun" to "Unicorn".

Back in the 1980s when I came up with the idea of a 4x4x4x4 4D chess variant, in a different city than I am now, I had borrowed a library book on fairy chess which I recall only a very small number of things about (not including the title or the author's name). One thing the book showed was a diagram for a 5x5x5x5 4D chess variant, with the 4D fairy piece type Balloon included. As an aside, I at once preferred a 4x4x4x4 board concept, to have an equal number of light and dark squares, but later I saw that 5x5x5x5 at least often allows a knight more legal moves depending on location.

The book also mentioned the "Unicorn" as a 3D piece. It likely matched wikipedia's description of its movements. If so, I'd note that nowadays this use of "Unicorn" doesn't quite make so much sense to me, however, since the mythical beast is virtually a horse, and it thus seems desirable to me that any such named piece would have some knight-like property to it (regardless, in the 1980s, not thinking of this, I wanted to use the name "Unicorn" for a piece, since it's charming for a name). In spite of this, I'll drop the use of "Nun", as mentioned.

Kevin Pacey wrote on 2015-10-30 UTC
By editing my submission I've now added more diagrams, including one illustrating possible legal 4*Chess Pawn moves.

Kevin Pacey wrote on 2015-10-30 UTC
Hi Ben

Fwiw, here's a wikipedia link that mentions the Balloon and various uses of Unicorn that they are aware of. I'm virtually new to fairy chess, especially terminology, so I don't know how much weight wikipedia can be given:

I'll see if I can clarify 4*Chess pawn moves more by editing my submission at some point. I made an attempt when I tried unsucessfully to post my first comment, and was told I wasn't signed in (somehow).

Ben Reiniger wrote on 2015-10-30 UTC
The "nun" is commonly called the unicorn in 3d games, and I think it's reasonable to extend that name into 4d games.  (Do you have a good reference for the name "balloon"?  I've only ever seen it called that in one place.)

The initial setup is interesting; all the pawns are protected--many of them by the army of balloons--and they smother many of the initial lines.

I don't completely understand the pawn movements.

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