Comments/Ratings for a Single Item

Well, I guess the atom describing the next leg defines the eligible directions. One could define the smallest deflection as forward. If I am not mistaking this would mean that transitions from one oblique atom to another would use the corresponding element from the set of eight, oblique to orthogonal would go along the largest coordinate, and oblique to diagonal would stay in the same quadrant. Other transitions would all be 'degenerate', i.e. 'forward' would indicate two symmetry-equivalent continuations of orthogonal or diagonal atoms, wheter this continuation is of the opposit kind or oblique.

Yes, that sort of is my thought (keeping "forward" within the same 45-degree arc). So the [Z?B] you mentioned earlier would be the Tiger as listed, [C?B] the Astrologer, and [N?R] the game's Pegasus. The Octopus from Octopus Chess could be something like [F&nD?R][W&nA?B].

In the current implementation a continuation leg would always need a directional modifier, as the default is 'every direction except back', just as in the 'a-notation' to which it is converted by a simple pre-processor. We could change that default into 'forward' (= outward), though. Then the Pegasus would indeed be [N?R], rather than [N?fR].

Note that the ? to make the continuation optional is only needed to include the first step, so one can write [F?R] for the Griffon rather than F[F-R]. Since the Octopus is not able to stop at the initial squares of the path (which by definition consists of the squares where it can be blocked), using the hyphen would be more natural: [F-W-R][W-F-B].

In the case of the Tiger from Tiger Chess, the author didn't use the word "forward" but "outward" instead. In my opinion, with that word the definition is clear and not really ambiguous.

With the understanding that direction specifications in a continuation leg must be interpreted in an orientation where the basic leap of the previous leg is 'forward', outward and forward mean exactly the same: continuation in as much the same direction as possible, given the difference between the leaps. But I think there would indeed be no ambiguity if K/Q-like atoms in continuation legs are avoided. For [N-Q] 'outward' would be ambiguous, as it would require some advanced geometry, which most people would not master, to decide whether the adjacent diagonal or the orthogonal continuation had the smallest angle with the N leap. In fact, after a C leap a W continuation would have the smallest deflection, while the F continuation would bring you at the largest distance from the square of origin (because F steps are geometrically larger than W steps), and both could claim to be 'outward' on that basis.

The point is that a general system must also be able to account for cases where the continuation is not the one that goes most outward, and there aren't enough spare lower-case letters to build a completely alternative system for indicating arbitrary relative orientations. So we will have to do with the familiar f, b, r and l, also in continuation legs. This doesn't seem a problem; even on one-leg moves 'forward' is to be interpreted relatively, namely w.r.t. the player.

Note that Charles Gilman proposed an equivalent definition of outward nearly ten years ago

As to [N-Q] and its like, why not just have it equivalent to [N-R][N-B]? After all, that would give symmetry with [Q-N] as well as making useful an otherwise useless definition (as anything involving the ‘advanced geometry’ would never result in a combination of orthogonal and diagonal moves, making [N-Q] a less elegant synonym for [N-R] (or another leap followed by B)) into a nice shorthand (much like Q itself)

Well, if we allow Q (defaulting to fQ) as continuation after an oblique, we should also be prepared to interpret other angular modifiers there. And we probably don't want [N-frQ] to default to [N-frQ][N-frB], as fr has different meaning on orthogonal and diagonal atoms.

We could treat K/Q after oblique as a degenerate 8-fold case, though, where f represents the nearest orthogonal and diagonal directions. That would amount to the same thing for the case you mentioned.

OK, the hyphen, not the Ampersand; there's not much discussion on the use of punctuation marks (other than the asterisk) in this description.

As to the "fbrl" problem, you're probably ahead of me here, but on non-initial legs they can just all be relative to whatever an unmodified, default "forward" would be. This, something like [C-bW] would be a Knight that cannot move to a space with a piece directly beyond it -- it makes a Camel's (1,3) leap, and then slides one space back toward its starting point.

For [N-Q] 'outward' would be ambiguous, as it would require some advanced geometry, which most people would not master, to decide whether the adjacent diagonal or the orthogonal continuation had the smallest angle with the N leap.

Another possibility is that [N-fQ] could be interpreted as a combination of [N-fR] and [N-fB]. I think of 'outward' in continuations as excluding any crossing of a queen's path from the starting square.

Another possibility is that [N-fQ] could be interpreted as a combination of [N-fR] and [N-fB]. I think of 'outward' in continuations as excluding any crossing of a queen's path from the starting square.

Pretty much exactly what I've been getting at. (If Q=BR, then [N-fQ] = [N-fB][N-fR].)

Pretty much exactly what I've been getting at. (If Q=BR, then [N-fQ] = [N-fB][N-fR].)

Yes, I didn't notice you'd said the same thing before I wrote that. The same would go for things like [D-fQ] or [F-fQ]. I've actually tried using [N?fB][N?fR] in games before, but I don't know if anyone else has.

The same would go for things like [D-fQ] or [F-fQ].

Oh that's neat; gives a nice shorthand way of describing the likes of Tripunch pieces.

Though it's perhaps not 100% clear (which might be what H.G. was getting at?) how this interacts with e.g. `[K-fsQ] for the gorgon (gryphon/manticore compound)

Thinking more, interpreting fQ as fBfR wouldn't match the use of fK to specify complex paths. I just noticed, [D?fsfQ] works as expected, but [N?fsfQ] does not. Another possibility is to allow multiple continuation options, as in [N-fBfR]

Betza notation has four directional notation systems: for 4-fold or 8-fold atoms, and each of those in a degenerate (2 directions are equally 'forward') and a non-degenerate version. As specification for the initial direction, diagonals and obliques are degenerate, orthogonals and K/Q ('compounds') are not. XBetza uses the rule that continuation diections are always specified in an 8-fold system, to allow 45-degree turns.

The XBetza a-notation only allows continuation with the same atom, or a 'rotated' or 'range-toggled' version. With the bracket notation one can specify transitions between arbitrary atoms. We can divide the atoms into two groups: oblique and non-oblique. A simple rule is that a transition that stays within the group uses the non-degenerate 8-fold directional system, and transitions between leaps from a different group the degenerate 8-fold system. This avoids the nitpicking (= 'advanced geometry') for whether the adjacent diagonal or orthogonal is most forward after an oblique leap: they are made equivalen by definition even when in reality they are not. Just like in a transition between different obliques the one labeled 'forward' does not go in exactly the same direction. For a transition from orthogonal/diagonal to oblique the pairs of directions are truly equivalent.

If branching in an oblique to compound transition is not desired (which would usually be the case, as the two paths would not be symmetry equivalent), this can be solved by using an orthogonal or diagonal atom as continuation, rather than the compound. One direction in the pseudo-equivalent pair will always be orthogonal, the other diagonal. This avoids the need for using fl and fr, which would pick non-equivalent continuation for the adjacent directions in an oblique. (Which could be solved by using fq or fz instead, but most people would experience that as rather obscure.)

This 'chirality problem' would still exist if we wanted to indicate a continuation direction other than f in descriptions like [N-rR]: this would select moves of a different shape for the hlN and hrN chiral subsets, and would have to be written as [N-qR] for continuation in the 'outward' direction in the short dimension of the oblique leap.

A consequence of defining f as default in continuation legs is that it becomes difficult to indicate moves that can continue in arbitrary direction. Such as Tenjiku Shogi area moves or Lion hit-and-run captures. But since the function of the a has been taken over by the hyphen (or question mark), we can redefine its meaning inside the brackets as "any direction except exactly backwards". So a 3-step area move could be [K?aK?aK], and the Lion hit-and-run [cK-aK].

This mentions "pieces that push other pieces," but there's no instruction (or case study) on how to implement that, at least that I can find. I'm thinking specifically of ways to push (or pull, or otherwise move) opposing pieces.

Well, you first move to the square where you want to push the piece to, and then use an 'unload' leg to capture the piece to relocate it there. E.g. a Pawn that can pushe enemy pieces with its non-capture would get an extra fpafabucW to first hop over the pushed piece, and then swap with it.

Aha! Thanks!

I potentially have something a bit more complex in mind, but this will do for that.

I now implemented more sensible defaults for the bracket notation. Rather than having an omitted directional specification in a continuation leg mean "all except to where you came from" (as it would in XBetza), it now assumes f (i.e. most outward) or, in the special case where you switch between diagonal and orthogonal atoms, fs (45-degree bend either way). A pure b is interpreted as bs in the latter case. (But inward continuations would almost never be used.) Other explicitly described direction sets will be taken at face value, even if they specify a direction that is incompatible with the atom that was mentioned; the atom is only taken into account for supplying a default.

This is more suitable for the cases for which the bracket notation is mainly intended, namely describing a single path or a symmetrically forked path. The Griffon can now simply be described as [F?R]; because the directionality of the atoms is now taken into account, this would be interpreted as [F?fsR].

The case of "all directions" can now be obtained by a new directional modifier a. So you could write [K-aK-aK] for the Tenjiku-Shogi area move, and [cK-aK] for a Chu-Shogi Lion's hit-and-run or double capture.

Just for general reference, I thought I'd go through the page and sort out all of the letters currently used in the code:

A - Alfil (2,2)
B - Bishop (FF)
C - Camel (1,3)
D - Dabbabah (0,2)
F - Ferz (1,1)
G - Tripper (3,3)
H - Threeleaper (0,3)
I - Imitator
J - alt Zebra
K - King (WF)
L - alt Camel
N - Knight (1,2)
O - Castling
Q - Queen (BR = FFWW)
R - Rook (WW)
U - Univeral leaper
W - Wazir (0,1)
X - +3 ortho
Y - +2 diag
Z - Zebra (2,3)

a - again
b - backward
c - capture
d - destroy (friendly capture)
e - en passant
f - forward
g - grasshop
h - half
i - initial (or “iso” in a sequence)
ii - initial (where any such piece starts)
j - jumping
k - king (delivers check)
l - left
m - move only
n - non-jumping
nn - non-jumping, allows en passant
o - cylinder (l/r)
oo - toroid (l/r & f/b)
p - hop
q - circular (rotates direction)
r - right
s - sideways
u - unload (position switch)
v - vertical
x - excite (move induction)
y - fork (in a sequence)
z - zigzag

I ignored the bracket mode and such things that aren't really codified yet (as much as I look forward to that).

K = WF, not AF.

It might also be worth to mention where character doubling can be used to slightly alter the meaning. Directional modifiers can generally be doubled to prevent they would be combined with a perpendicular one for indicating an in-between direction. In addition oo = toroidal wrapping, nn = non-jumping and generating e.p. rights on the squares passed through, ii = only on the squares where such a piece started. And proposed cc = rifle capture as automatic side effect when there is something to capture there.

So unassigned capitals currently are E, M, P, S, T, V. Perhaps P would be a useful shorthand for the Pawn move, which has a bit of a lengthy description in basic XBetza. E.g. P3 could be taken to mean fmWfceFifmnW3, a Pawn that can step up to 3 forward initially.

The only unassigned lower case are t and w. Betza used t as 'then' in a kind of bracket notation, but this seemed redundant, as the brackets already imply it. At this point he was abandoning his original goal of only using alphanumeric characters in the notation by allowing the brackets, but was still too much leaning towards the old ways to accept punctuation in general.

I coined the idea of using M (mirror) for pieces like the Ultima Chameleon, which much borrow the move set of their victim to capture. And to use E in the bracket notation (where each leg can use a different atom) as a test for whether you are on an edge square without moving.

I corrected the K (I don't know why I said WF) and put in the double-characters.

As for your other ideas:

Would ccN then become a substitute for cabN?

With P, how would something like a Berolina Pawn be done?

I still support the M proposal, as long as it can be modified to enable Friends and Orphans (unless you think one of the other capitals would be better).

Perhaps t (turnabout) could be used for both of those purposes: tP2 would be the Berolina Pawn, tM the Orphan, ttM or dtM the Friend (though more likely cxM for Orphan and dxM for Friend). It could also be used in brackets (test) to check and see if a certain relative position is off the board. ([tW2?bN] would allow a Knight's move away from the edge only within two spaces of it.) Probably it could be used for other things with other atoms outside brackets.

A thought on w -- maybe that could be used as a modifier to directions that are always in relation to White. That could, among other things, simplify the Castling in games like Short Sliders (and the Leapers Who Love Them). Currently that's KirO2ilO3 for White and KirO3ilO2 for Black; it could become simply KiwrO2iwlO3 for both. It would also still allow w to be used for other purposes when not followed by a direction (lwB would do something different from wlB).

Those last two parts are just spitball musings, of course.

Addendum: I just had a weird thought for a piece called a Paparazzo, which can mirror the move of any piece that moves away from it in the preceding half-turn.

The Interactive Diagram solves the castling problem by adopting the general convention that left and right for black should be interpreted in the context of the symmetry parameter; for symmetry=mirror they should be flipped. Before that I had an explicit parameter castleFlip, but this is now automatically set according to the value of symmetry, if no explicit value was given. In fact it would be best if there was left-right flip for all moves in that case, but I haven't gotten to implementing that, as pieces with left-right asymmetry are very rare, and the few (Shogi) variants I am aware of that do have them use symmetry=rotate rather than mirror.

I think ccN would only be useful as part of a multi-leg move, because it is not just an abbreviation for cabN. The latter would force you to capture the a piece on the detour, and if there was no enemy piece there, would not allow the move. The idea of ccN would be that it must make the detour if there is something to capture, but can be ignored if there isn't, so the remainder of the move can still be made. So apart from standing for cabN, it would also allow mabN (detour over empty square), oabN (in case the detour would leave the board) and dabuN (hop over a friendly piece, disguised as destroying it and then putting it back on the same square). In this meaning an isolated ccN would not just allow rifle capture, but also a turn pass in case there was a friendly piece, empty square or board edge within Knight range. This is almost certainly not what you'd want. But in a multi-leg context such as [Q-fccK] it would describe the Advancer: move as Queen to an empty square, and mandatorily remove an enemy on the next square if one is there, but never mind if there isn't such an enemy (or such a square), and doe the Q leg anyway.

Understood! That's a pretty good abbreviation for mcoabNdabuN, then.

And now I'll go fix the Castling on Short Sliders, to how it should be....

But if a certain piece always goes in relation of White (say, an "East Wind" that always points toward White's left), that would use symmetry=rotate for the piece?

Well, the symmetry parameter primarily controls how the black pieces are placed in the initial setup, in relation to the white pieces, so you only have to specify the locations of the latter. Usually the only move with left-right asymmetry is castling, because on boards with an even width the King necessarily is placed asymmetrically, and some variants desire a symmetric result. Unlike rotating the board, mirroring it swaps the notion of left and right, which are concepts defined relative to forward and backward (which are the two directions that are really swapped). So an asymmetric piece that moves, say, diagonally inward from h1 and h8 would move fl for white, and fr for black if l&r was defined from the player POV. So they would then need to be different piece types, which then spoils the mirror symmetry of the placement. In a rotated setup the corresponding black piece would be on a1, and diagonally inward would still be fl. So there the problem does't exist. So far I have seen such asymmetric pieces only in Shogi variants, (e.g. Left and Right Chariot, or Quail), which tend to have rotation symmetry of the initial setup, so that it wasn't really a problem.

Would there be sufficient utility for a null-move atom (say, S for "stay")? It could be a handy shorthand for the Japanese Lion or the Zero, rather than mabK, but I'm not sure what other utility it would have... maybe to activate spells or area-effect captures without actually moving? (Now that I think on it, it might be simpler to just allow K0 for that sort of thing.)

I also had hoped that multiple uses of j on a slider would continue to increase the size of the initial leap, such as jjB (or something similar, like j2B) where the Bishop's first step is three spaces, but no such luck. I guess bracket notation ([nG?fB]) will have to do for now.