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4*Chess (four dimensional chess). Four dimensional chess using sixteen 4x4 boards & 96 pieces. (4x(4x(4x4)), Cells: 256) [All Comments] [Add Comment or Rating]
Ben Reiniger wrote on Fri, Oct 30, 2015 04:40 AM 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.

💡📝Kevin Pacey wrote on Fri, Oct 30, 2015 06:08 AM 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:

https://en.wikipedia.org/wiki/Fairy_chess_piece

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).

💡📝Kevin Pacey wrote on Fri, Oct 30, 2015 05:27 PM UTC:
By editing my submission I've now added more diagrams, including one illustrating possible legal 4*Chess Pawn moves.

💡📝Kevin Pacey wrote on Sat, Oct 31, 2015 06:07 AM 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 Sun, Nov 1, 2015 01:31 AM UTC:
I've edited a couple of my comments & original submission for 4*Chess, in case anyone hasn't noticed.

Ben Reiniger wrote on Thu, Nov 5, 2015 05:16 PM 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 Thu, Nov 5, 2015 08:02 PM 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 Thu, Nov 5, 2015 08:25 PM 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 Thu, Nov 5, 2015 08:39 PM 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.

💡📝Kevin Pacey wrote on Thu, Nov 5, 2015 08:51 PM 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 Sat, Nov 7, 2015 04:10 AM 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 Sat, Nov 14, 2015 09:36 PM 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 Sun, Dec 20, 2015 07:39 AM 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:

http://www.chessvariants.com/index/msdisplay.php?itemid=MStesschess

🕸Fergus Duniho wrote on Sun, Dec 20, 2015 02:08 PM 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="/play/pbm/diagram-designer.php?submit=Update&code=rnbqkbnr-8%2Fpppppppp-8%2F8-8%2F8-8%2F8-8%2F8-8%2FPPPPPPPP-8%2FRNBQKBNR-8%2F-----------------%2Frnbqkbnr-8%2Fpppppppp-8%2F8-8%2F8-8%2F8-8%2F8-8%2FPPPPPPPP-8%2FRNBQKBNR-8%2F&shape=square&scale=40&group=Chess&set=abstract1&files=1a+1b+1c+1d+1e+1f+1g+1h++2a+2b+2c+2d+2e+2f+2g+2h&ranks=1A+2A+3A+4A+5A+6A+7A+8A++1B+2B+3B+4B+5B+6B+7B+8B&font=Verdana&point=12&cols=17&board=10.01.&colors=339933+CCCC11+22BB22&bcolor=111199&tcolor=EEEE22&bsize=16&bgimage=maple-walnut.png&nextfile=50+0&nextrank=0+50">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.

Joe Joyce wrote on Sun, Dec 20, 2015 07:07 PM UTC:
Here's a simple board you can use - just remove my pieces for this unsuccessful game, and place your own. And welcome to the ranks of those who have tackled 4D chess! 

/play/pbm/play.php?game%3DChess+on+Two+Boards%26settings%3DC02B

💡📝Kevin Pacey wrote on Mon, Dec 21, 2015 06:26 AM UTC:
Hi Fergus

I've now added a Diagram Designer generated diagram to the Setup portion of my 4*Chess webpage submission, by modifying your example 4-dimensional chess diagram through heavy trial and error to be pretty much the way I wanted (I had to use an even number of Columns to get the square colours alternating the way I wanted to for all the 4x4 mini-boards, though this resulted in thicker margins between the 16 mini-boards, which I wasn't too concerned about). 

I'm hoping there is a way to use the Designer's HTML code I've cut & pasted into my submission, by (during possible editing of my submission in future) cutting and pasting the HTML code of this existing diagram I generated into the HTML code box of the Diagram Designer (i.e. if and when I start up the Diagram Designer webpage from scratch). That is, I'm hoping I can do so by then getting the Diagram Designer to somehow update its generated tentative diagram (for 8x8 chess, by default) using the cut & pasted HTML code. Then I can make a new diagram I like for my 4*Chess variant (for example) without a ton of modifications by having to modify the FEN string (along with making necessary field changes) starting from scratch at the default (8x8 chess diagram). Do you know if this would be possible?

In any event, for at least the time being I can leave in the 20 or so crude diagrams in my submission, whether or not I add more Diagram Designer generated diagrams at some point.

🕸Fergus Duniho wrote on Mon, Dec 21, 2015 01:37 PM UTC:
There are two ways to get thinner borders between 2D sections. One is to change the checker pattern, which is what I would do. The quicker way is to reduce the border size, but that will also reduce the size of the outer borders, where the coordinates are written.

💡📝Kevin Pacey wrote on Mon, Dec 21, 2015 07:48 PM UTC:
I'm okay with leaving the diagram as it is, if it's not too objectionable. I tried changing the Border Size using the Diagram Designer as suggested, but only the outer left and outer top border were affected, i.e. otherwise not at all changing the thicker spacing between the small 2D boards (which I called mini-boards). At least I was able to make much use of the HTML code string I had pasted earlier into my webpage submission page, by cutting & pasting the part relevant to the FEN string, when using the Diagram Designer from scratch (I deleted certain parts & replaced then with '/' where I had to, though). I did something similar in the way of cutting & pasting the file and rank labels. Otherwise I had to set the fields (e.g. for the number of Columns) from scratch again where appropriate. The whole process was not nearly as time consuming as when I generated my diagram the first time from the Diagram Designer.

In spite of the above, I am wondering if there is an existing or unwritten convention as far as how the checkering of the 2D boards alternates. Almost all the webpages with 4x4x4x4 4D chess variants on this website were submitted to have the checkering alternating kind of like in your example, Fergus, much like there is a convention for this in 3D chess variants apparently. Still, I did notice one 4x4x4x4 variant on this website that had the 2D boards checkered the way I have them at the moment (some other such 4x4x4x4 variants had diagrams that used no colours for checkering at all!). As I say, do you or anyone else have strong feelings on the checkering of the 2D boards? Personally, I found calculating when playing decades ago using the checkering I have for 2D boards to be natural enough in that it did not offend my sensibilities somehow, at least.

🕸Fergus Duniho wrote on Mon, Dec 21, 2015 10:29 PM UTC:
While I'm not familiar with what convention there might be, what I consider logical is to checker it in a way such that anytime a Rook makes a one space move, it changes color. So, 2D sections of the board would alternate their checker pattern in what is itself a checker pattern. This checkering pattern would also keep Bishops on the same color.

🕸Fergus Duniho wrote on Mon, Dec 21, 2015 10:35 PM UTC:
The Unicorn piece you're using is for David Paulowich's Unicorn, which moves as a Bishop or a Nightrider. That's why it combines the Bishop and Nightrider images. It does not represent the 3D Unicorn. The Unicorn in the Alfaerie set would be better suited, because it is just a horned horse.

💡📝Kevin Pacey wrote on Tue, Dec 22, 2015 01:28 AM UTC:
Hi Fergus

I couldn't somehow see at all which option possibly corresponded to a Unicorn (or 'horned knight') in the Alfaerie set as given, if I'm using the Diagram Designer right, though I'm not sure what you meant by 'horned knight'. However, in choosing 'Cazaux Graphics' as a setting for the 'Set' field in the Designer, I found what I thought were nicer images for both the Unicorn and the Balloon, for within what I gave as a second Diagram Designer diagram for the start position of 4*Chess (in the Setup box) of my once again edited submission for it. I left in my first Designer generated diagram, using the Abstract pieces and different 2D Board checkering patterning (for purposes of comparison), for the time being.

Regretably, my earlier 20 or so crude diagrams all have the checkering pattern I initially preferred for 4*Chess, though I imagine it won't be too much trouble to compare them with any future Diagram Designer diagrams that I add to my submission, if I leave in all or some of the crude diagrams indefinitely.

🕸Fergus Duniho wrote on Tue, Dec 22, 2015 01:59 AM UTC:
There are so many Alfaerie pieces, you won't find them all in the same set unless you use a really large set, such as "Alfaerie: Many" or "Auto All Alfaerie". The Unicorn can be seen in the "Alfaerie: Animal Pieces" set, though I don't think anyone has added a Balloon piece to the Alfaerie set.

💡📝Kevin Pacey wrote on Tue, Dec 22, 2015 05:10 AM UTC:
Refering to my last post, what I chose to represent a Unicorn seems fairly okay to me, as the animal (whatever it is ) at least shows one pretty straight looking horn as far as I can tell, though at the least the head is rather thick for it to be horse-like - but possibly this is a blessing when trying to tell the piece easily apart from a knight in a given diagram. 

In any case, I saw that the Diagram Designer setting (for 'Set') that is 'Small pieces for large boards' actually has a Unicorn (knight with one horn) perfectly represented (but nothing available resembling a balloon).

Out of curiosity mainly, can you tell me if there is a simple way to include (on one or more cells represented within a single diagram generated by the Diagram Designer) just one fairy chess piece type's image from one setting for 'Set', besides using all the other fairy chess piece type images from one other setting for 'Set' (e.g. to switch just the piece image I used to represent Unicorns with the Unicorn image from 'Small pieces for large boards', if I decided to)?

💡📝Kevin Pacey wrote on Wed, Dec 23, 2015 05:46 AM UTC:
I have now replaced most of the old crude diagrams in my 4*Chess submission with Diagram Designer generated ones. That is, except for leaving in the one for the Setup position (now with appropriate alternating square colour patterning), and leaving in the ones illustrating legal moves by individual pieces on a vacant 4D board (these are also corrected for patterning), as a possible aid to the viewer. 

I may have missed how, but after some reading of the documentation I could not see a way for the Diagram Designer to show non-piece symbols on the actual board cells in a generated diagram, such as showing a letter 'X' (e.g. I used such in my crude diagram of a 4*Chess King's legal moves), though using the Designer for this purpose was not much of a priority for me. In addition, I have slightly altered the 4D board notation system I used for the diagrams, in attempting to improve them in this regard.

💡📝Kevin Pacey wrote on Thu, Dec 24, 2015 08:23 PM UTC:
Earlier I wrote:

"...what I chose to represent a Unicorn seems fairly okay to me, as the animal (whatever it is ) at least shows one pretty straight looking horn as far as I can tell, though at the least the head is rather thick for it to be horse-like - but possibly this is a blessing when trying to tell the piece easily apart from a knight in a given diagram."

Fwiw, in looking up the mythical animal 'Unicorn', I discovered that sometimes one can be goat-like (instead of horse-like):

https://en.wikipedia.org/wiki/Unicorn

An example of a goat with a beard, such as what might be shown by the animal symbol I used to represent a Unicorn in my diagrams, would be an Irish white goat. That's if ignoring the possibly single horn in my chosen animal symbol (to perhaps tell better if a single horn is the case, I think I can actually make out part of the animal's far eye by looking closely, in the case of a White piece version at least). Within the following link besides the Irish white goat I also noticed examples of another breed, namely a mother with her kids, which had both thick heads and thick necks:

https://en.wikipedia.org/wiki/Goat#Anatomy_and_health

One more thing I came across elsewhere on the web was a mention that the length and thickness of a Unicorn's horn can vary.


Disconcertingly for me, all this seems to go against a convention in fairy chess circles to show Unicorns as horse-like. That is, as Knights with long thin single horns that are as long as, e.g., from an eye to the mouth. However, I was happy to have any sort of moral support for my depiction of a Unicorn (aside from a Balloon) in my diagrams, with the available Diagram Designer piece sets that I had to choose from. :)

[edit: in checking the 'Properties' of the animal image shown as a Unicorn in my diagrams, it's used to represent a Gnu normally it would seem. Joke's on me. :) ]

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