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Fractal Chess. Missing description (2x(8x8), Cells: 80) [All Comments] [Add Comment or Rating]I don't get it. Geometry and rules need to be more clearly explained, with examples.
Joe Joyce wrote on Sun, Sep 17, 2006 04:07 PM UTC:This seems very interesting but I don't see exactly how it works. Is it really a 3D game played on 2 boards, like Alice Chess, except changing boards is voluntary, or is it something else? The description indicates it easily could fall into that controversial area of '4D' games, as it seems you describe a variant played on 2 totally different 2D boards, with free movement between them. Or even 1 standard 2D board, and 1 maybe 3D-mimicing smaller board. The 16 square 4x4 board does have 2x2 'subsets' of squares within each square, if I've read everything right, or does it? Depending on the exact movement rules, the game/board you describe could act as a 3D, 4D, or even 5D playing surface. Personally, I hope you are doing a 'higher-dimensional' game, and would refer you to Parton's Sphinx Chess, Aikin's Chesseract and my own Hyperchess for 3 similar '4D' treatments. I would strongly recommend looking at LL Smith's and Dan Troyka's 4D, 5D, and 6D games, which illustrate rather nicely the use of higher space dimensions in chess, even though some see them all as convoluted examples of 3D. Welcome to the debate.
You'll soon get the ZOG file available, so that you could figure out what
it's all about. In some loose sense, the game would have a fractal
dimension, not an integer one ! The second board does have 4x4 squares,
each pointing to 4 sub-squares on the other board. Does this make it a 4D
like game ?
As you pointed out, it's not Alice Chess related as you're not compelled
to switch to the other board. I just wanted to allow larger movement on the
larger board to be mapped to the smaller scale board.
I will consider the games you listed (sphinx, hyperchess,...) with
attention.
You'll be perhaps interested by my 8x8x8 'cross3D chess' game, and the
mapped version on two boards which I called 'mapped chess'.
From what I can figure, it appears that the 4x4 field is tied to the 8x8 field by its single cell to a 2x2 group on the latter. So that the a1 cell on the 4x4 field is tied to the a1, a2, b1, and b2 cells of the 8x8 field. So a piece on the a1 cell of the 4x4 field would be able to move to an empty cell on either a1, a2, b1 or b2 of the 8x8 field; and a piece on a1, a2, b1 or b2 of the 8x8 field is able to move to an empty cell on a1 of the 4x4 field. This is why a bishop is able to break its diagonal pattern. The wording of the rules is a little hazy. Would not pawn promotion be allowed only on the 8x8 field?
Hi, Stephane. Exciting idea here. We've been having a bit of trouble sometimes uploading some things, especially zrf files. Could you please post the url for your zrf file here meanwhile? I would appreciate that.
Jeremy, I'm afraid I can't post the url for technical reasons. I hope you'll be kind to wait for the ZOG I sent to be published on these pages. Anyway, thanks for the appreciation that far
The ZOG file is available right now as a new game on 'http://www.zillions-of-games.com' I hope it will be soon available on these pages too as a separate item.
In reading the 'encyclopedia of chess variants' by Pritchard, I found a similar (but not reducible to) game to mine called 'Sub-Chess' by Chebotaryov in 1988. His board contains a subset of 8x8 half-squares in the 4x4 larger middle squares, where pieces may move alternatively on both. So I must give him the origine of the concept.
Stephane Burkhart, who posts Mapped Chess this week, made the last Comment in his own Fractal Chess from 2006: ''In reading the ECV by Pritchard, I found a similar (but not reducible to game to mine) called 'Sub-Chess' by Chabotaryov in 1988. So I must give him the origine of the concept.'' In turn, Mapped Chess and Fractal Chess have their comparabilities for follow-up Comment. Nowadays only a year later, the prolificists (not referring to Burkhart's 5 games at all of course nor singling any one out) do not simply thank for the information about a related (earlier) form. Not having researched their topic, they increasingly are defensive or annoyed about comparable prior art called to attention. People have been at this for at least 1500 years, and madly for ten years(25 years counting Betza), so Burkhart's is a good reaction, loosely ''How interesting great minds can think alike'' in praise(respect) for the priority. Cleverly here in going from larger to smaller scale a la Fractal, same-side opposite-colour Bishops can end on same colour. ''See the consequences at smaller scale.'' Ingenious and maybe at first opaque in the detail requiring another Comment along with the Mapped one. These CVs in style are not far removed from Ralph Betza and J. P. Neto and David Howe in mixing the abstact with the specific embodiment.
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