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Multi-positional, I reckon, Mr. Duke, is an entirely different thing from
the rest, which can be established in my said hierarchy. It is like a
sub-species, as any piece can have such quality and the rest is the same.
Now that the hierarchy is established, also, I wonder what new cousins
pieces could have.
Leaper/Stepper
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??? Multi-Path (must have at least one clear path)
___|___
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??? Planar (must have all clear paths)
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??? Rider/Slider (must travel along one axis only)It is good challenging practice to have alternate schema. I know a certain college biology professor who once opted to be handed down from ph.d. program because of their obsession with their one and only taxonomy, despite obvious contradictions. I think we can fill in the three question marks. Alongside multi-path might go Joe Joyce's ''Sequential'' like Bent Shaman. Sequential is not in Howe, or Neto, or Laukamp, but it's there and needs accounting. The appropriate spin-off of multi-path, sister of Planar would be Hopper, a kind of opposite of planar and off multi-path because the intervention facilitates not detracts, for one thing. That leaves the accompaniment to Rider/Slider. You know, I think multi-positional plugs right in there! There are siamese twins inevitably across and along generations not strictly following any full logic of subclasses. That's why I am also just making one differentiable list of about 15.
You're right; there aren't strict subsets and we don't know all the
different possible piece types. When I heard multi-positional, I was
thinking of something like a Wall that takes up two squares. Perhaps you
mean a piece that can move from multiple positions as origin, viz
Fourriere's Wizard. This brings us to a new division, variable-destination
pieces and invariable-destination pieces. An independent-destination piece
could always move to the same squares. Dependent-destination pieces move to
different squares based on certain variable statistics. The most obvious
dependent pieces are those that have movement trace a path from their
current square. An alternative piece would be the Loner, which moves to any
squares that have a piece density of <25% as calculated from an average of
all possible 3x3 rectangles on the board. It becomes trivially more
powerful toward the endgame.
Joe Joyce wrote on Sun, Aug 30, 2009 03:26 AM UTC:About a third of the way into A Taxonomy, by David Howe, the shaman and hero are described in general under Complexity, Compound, Inclusive. Following is the relevant section: 'An Inclusive Compound piece has the option, on any one move, of moving as one or more of its component piece moves. Such pieces tend to be extremely powerful and should be used with care. eg. a Super Cardinal may move either as a Bishop or as a Knight, or may move first as a Bishop followed by a Knight move (in the same direction), or may move first as a Knight followed by a Bishop move (in the same direction).' I can offer a piece that isn't in David's work though: a chesimal; a 'piece' made up of several chesspieces, generally of a few different types, that all may move [1 at a time, legally] every turn, but must all basically be in contact with [touching] each other at the beginning and end of the move. This 'piece' can take hits; that is, it can lose some of its units, and continue to exist, still moving all its remaining units. And it can capture as many pieces as it can legally move onto in one turn. :-) I suspect others, like Mats, for example, might offer other types of pieces, but it may depend on just how broadly or narrowly you define categories and subcategories. Enjoy.
The Emperor is non-autopositional variable piece, moving to any square defended by a friendly piece. The counter of the Emperor would be the Anarchist, which moves to any square attacked by an enemy piece. Anarchists would make for much more aggressive games by discouraging defense. The fluidity would be too high for most initial positions, so there could instead be Libertarians, moving to any square attacked by two enemy pieces. Between an Emperor and an Anarchist would be a Moderator, which moves to any square both defended and attacked. Pieces of this sort make for careful positioning, and are best suited for sparse boards.
It comes as a surprise what CVs mean to other participants unless there is some commonality. Slider is spider in 8 directions. Leaper is creeper in etymological descriptive child's play. Not everything thought up deserves the light of day. Martin Gardner wrote 25 years ago, ''Since we can invent bizarre chessmen that move according to any specific set of rules, the range of quadraphage-type games obviously is unlimited.'' Squares are infinite, and pieces are infinite. CVPage never did its job to find which-other taxonomy may help more. Each piece can be a piece-type category unto itself, so classes are infinite too, like boards. The more specific, the fewer members -- dilemma of categorization. Taxonomy is another game, classification by geometry, having utility more organizable than word-games, but less so than star-types or biological kingdoms, a middle ground. Super-taxonomy would account for history and complementarity too. The base is not formalism, let alone constructivism, but platonism. These things are real, real as the nose on your face. Once a construction establishes, it obliterates a thousand others. After this comment the particular will always take precedence. In fact, that is a new definition of Chess: amplification of the specific instance by a leap of faith for reasons of...for reasons...for Reason, leave it at that. Faith in Reason.
Here is Tetraktys I invented when Lavieri once called for Chess < 10
squares. http://www.en.wikipedia.org/wiki/Tetraktys
Above is outside link, below is the CVPage new ''CV'':
________._______ Tetraktys is played in the 9 triangles created by the
______.___._____ 10 dots. There are two piece-types A and B. A moves
____.___.___.___ through sides internally adjacently one space -- like
__.___.___.___._ a normal chess piece. B moves through sides externally
(#5,6,7,8, &9 cells are lowest above.) either one or two spaces away at
option. Each side has one A and one B. Label the cells {1;2,3,4;5,6,7,8,9}
left to right top down conveniently. They would be equivalent to
5;762;98431 and also 9;487;13265. So for example, with the first scheme,
from 5 A can move to 6 only, and if B were there, B can move from 5 to any
of 1, 2, 7, or 9. There are three internal triangles which more mobile B
yet cannot reach off-limits because having no outside border. Object and
victory conditions are either Stalemate, where opponent has no move, or
else more elegant Double Adjacency. Starting positions: Red B1 A4 and Black B9 A7. Piece density 4/9 = normal 44%. Power density obscure. Sides
alternate in series of twelve games. Double adjacency at start or finish of turn is the preferred win
condition. To lose so, it means your either A- or B-piece must move adjacent to both
opponent's A and B across internal sides, or they to you in the victory. Corners covered, 1, 5, and 9 is considered Double Adjacency. So watch to be careful of
adjacency.
I switched starting array both sides A and B as intended, with the 'B's initially cornered for better action. 'B' at 4 cannot move to 2, only 1 and 9, because that is where one or two borders away go; Triangle 2 would be 3 external sides removed from 4 and illegal. Also any 1,5,9 is Double Adjacency at start or finish of any turn by notional externalities. That should be it for Tetraktys. More cells, triangles, would be interesting up to a point. Five stars add 7 cells for 16-triangle board. Then six stars add 9 more cells for 25-triangle board. Then seven stars add 11 more cells for 36, eight 13 for 49, nine 15 for 64 triangles. Q.E.D. These would not be for large or normal Chess-like game just the limited study ones, because the outside moving, enhancing up to 25 or 36, starts getting distracting and artificial. Potential thousands of non-trivial games exist on nested equilateral triangular sizes 16 through 49, latter eight-starred. Please proliferate in kind.
The *GARGANTUA*, played in France until 1683, is a sequential eight-stepper of different component legs. (Http://en.wikipedia.org/wiki/File:Gustave_Dor%c3%A9_-_Gargantua.jpg, Http://www.sosort-lyon.net/FP/images/gargantua.jpg -- Rabelais; http://ebooks.adelaide.edu.au/r/rabelais/francois/r11g/book5.25.html.) Before returning to Joyce Daisies and Gilman suffixes, Binary 1000/0000/0000/0000 is 32,768, to represent 32,767 new piece-types never made before this comment, because let's use 0111/1111/1111/1111 instead conveniently. Using the digits right to left, Bit-place 1 is 1Wazir-0Ferz, Bit-digit 3 1Dabbabah 0Alfil, Bit 5 1FOKnight 0BOKnight, Bit7 1Camel 0Zebra, Bit9 1Rook 0Bishop, Bit11 1Cannon 0Canon, Bit13 1Mao 0Moa, Bit15 1CannonPawn 0QuadraPawn. The other Places/Holders/Bits/Columns/Spaces 2,4,6,8,10,12 and 14 tell as '1' the next step to the left is required, '0' not required for each up-to-eight-stepper Gargantua. Have around a Charles Fort 100x100 board in case. That's it. The actual number from 1 to 37,767 determines one clearly-defined piece-type. Each Gargantua can move eight component-steps for sure if unimpeded in actual board position, and each individual p-t probably allows earlier stops for player optionally each turn. ************* Generate a random number in context. The first sentence above has convenient 15 words bitwise of lengths 396265421(10)(12)2984 (for example 'the' = 3 = odd), which ''binaried'' as even or odd are x110/0010/0100/0100/. So just that one p-t out of 32,767 up to 8-stepper, moves in strict order per turn: Ferz then Dabbabah then Backward Knight, then Camel, then Bishop, then Canon, then Moa finally Cannon Pawn, with the ability to stop if wanted after Leg 1 or 2 or 3 or 4 or 6. A very typical move on little 8x8: c3-d4-f6-g4-f7-b3-g8-e7-d6. Frolov and Jaguaribe have done these Sequentials before, http://www.chessvariants.org/index/displaycomment.php?commentid=26370. Joyce is calling the same Super-class combination pieces. Future computers can be expected having a field day multi-stepping. Http://www.framingland-art.com/art/322864/Education_of_Gargantua_illustration_from_Gargantua_by_Francois; the Chess games of Gargantua, http://ebooks.adelaide.edu.au/r/rabelais/francois/r11g/book1.22.html. Http://www.corbisimages.com/stock-photo/rights-managed/42-16964968/illustration-of-a-scene-from-gargantua-by.
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