Presenting the "Pantheon" and a new family of pieces: Area movers.

There are three primary families of pieces (or movements) in the world of chess variants:

- Sliders: pieces that move along a path or direction, and that can be hindered very easily. For example, it is the case of riders such as the rook, bishop, queen (and one-step movers such as the pawn and the king also usually enter here).

- Jumpers: pieces that jump directly to a destination box, or jump to a set of boxes until they reach their destination. They are harder to block than sliders. For example is the case of knight, and other (unorthodox) pieces such as the wizard, the champion, etc.

- Hoppers: pieces that require the existence of obstacles to move. The best known example is the fairy piece "grasshopper".

But all these are directional or vectorial movers, ie, their movement is limited to a one-dimensional trajectory.
Today I show you a new piece concept and family: area movers.

Area movers are basically pieces of big movement range which movement is conditioned to all (or at least near) obstacles of the plane.

The movement of these is limited to a two-dimensional trajectory, or better said, these pieces have a "scanning area movement".
This type of movement is then very interesting for a 3D chess variant.

The way I describe this type of piece is hard to understand, but actually the concept isn't very complex, then I created a new piece named "pantheon" to explain to you better the concept.

Pantheon:

Name of the piece provided by Onesi*

The pantheon is actually the most simple area mover, and is analogous to the rook.
If we understand the rook as a piece with 1D trajectories, so pantheon is the 2D generalization of rook.

For example the rook moves following a linear (one-dimensional) trajectory, and his trajectory is ortogonal, of one coordinate: <n,0>: a vector.
If a piece is interposed in said linear trajectory, the rook will not be able to advance beyond said obstacle.
Rook movement:

The pantheon moves following a scanning area (two-dimensional) trajectory, and his trajectory is again ortogonal, but such ortogonallity isn't noticeable in a 2D board due to its nature. His movement is represented by two coordinates <n,m>: an area of possible vectors.
If a piece is interposed in said area (in this case, all de board), the pantheon will not be able to advance beyond said obstacle, that is to say, the pantheon will not be able to advance until the area projected behind such obstacle.

Pantheon movement: 

What are your thoughts?
Thank you for your attention.

That's not a bad concept. Instead of making a piece with a different type of move, the Pantheon has a different class of moves (not sliding, jumping, or hopping which nearly all other pieces do).

I think it's a little hard to describe though. Maybe it can be said that it can move "anywhere" but not in the orthogonal-shape shadow of other pieces like this (lines added on your diagram):

Is this correct? What about capturing ability? Is that a different definition?

That is correct.

For capture, it has the same movement.

Possibly my image can cause confusion about the capture mechanic of this piece (the opponent, red, piece is out of the movement range),  but imagine a rook: a rook can capture an opponent piece that is in a "obstacle position", ie, can capture a obstacle that is a opponent piece.

Basically this is the same in this case.

If one of obstacle of the pantheon is a opponent piece, the pantheon can capture said piece.

At a 2D board, there can exist area movers of limited range (unlike pantheon that is unlimited) as well as area movers that moves behind to the ortogonal projection of others pieces (ie, have a reversed movement, moves where a common pantheon can't move).

All these are based in the same type of movement.

Actually there can exist area movers with others types of movement mechanic, but not in 2D chess.

In a 3D chess, for example, it is added two new area movements types.

For explain it better:

The area movement becomes is actually a "plane movement", for example the pantheon can move in one only plane at a 2D chess (this plane is the board itself), but has 3 possible planes of movement in a 3D board (and these would be the x,y,0 horizontal plane and x,0,z and 0,y,z planes).

Remind that pantheon has a ortogonal movement.

Then, the other two new area movements would be "diagonal plane mover" and the "trigonal plane mover".

The diagonal plane or area mover would move through the three-dimensional board inside 12 possible planes!

And a trigonal plane or area mover piece would move through the 3D board inside 8 possible planes.

These two extra types of area movement can't exist in a 2D board since they need the existence of a volume.

In a 4D board, the thing becomes much more interesting, with more than five possible types of area movements.

It isn't all: "volume movers" pieces can exist in 3D and 4D chess boards!

So I'm still a little confused about your last diagram (with 2 black pawns, and 2 red pawns).

The way I see it, the pantheon cannot go in the "shadow" of one piece to capture another piece (just like a rook is blocked in one dimension).

I see the diagram like this: Red, orange and purple lines show the edge of the shadow. The three black pawns can be captured. But the red pawn cannot be captured because it is in the shadow of the g7 pawn.

Is this not correct?

That is correct.

Said red pawn can't be captured since is out of pantheon range, inside the "shadow" of another obstacle.

This is another example of how pantheon interacts:

Still a little confused about the meaning of the red pawns. From your diagram, can the Pantheon capture all the pieces with black lines going to it?

The way I understand it, the black Pawns represent friendly pieces, which is why their capture is not indicated. The red Pawns are opponents. But I think you are right: had all the Pawns been opponents, the Pantheon could have captured those you have drawn a line too.

The rule is that the Patheon can make any move or replacement capture that leaves the rectangle it 'sweeps' empty (except for its own presence).

This is a very nice, innovative idea. Like with sliders, you could have finite-range area movers. But they would have to be characterized by two ranges, a horizontal and a vertical one. E.g. a (5,3) area mover could make any move that sweeps a rectangle not extending beyond a 5x3 area. Ordinary (limited range) sliders would be (N,1) area movers.

You could also have diagonal area movers, which would sweep 45-degree rotated rectangles, paying only attention to occupancy of the squares of their own shade. Or area riders, which would make larger elementary steps that could jump over pieces (such as a (2,0) 'Dababba' jump), and apply the blocking criterion only to the squares they could visit. Or have 'lame' riders that would also be blocked by occupancy of squares they could not visit. You could also have 'area hoppers', which can only move if there remains exactly one other piece in the rectagle they sweep. It opens a whole new world of moves.

Note, however, that the term 'area mover' was already in use for Tenjiku Shogi pieces that could make multiple King moves per turn in varying directions (stopping at the first capture), and thus could reach any square in a certain area around them on an empty board. The name seems to fit the current invention better, however.

Red pawns are "opponent pieces" and black pawns are "friendly pieces".

Then, if all the pieces (even black) were opponent pieces, your assumption about pieces captures that you have indicated, is correct.

All these ideas are very interesting. 

 Huh... possibly I will change the name of this type of pieces to "surface movers", "plane movers" or "flat movers"; and more now that I am planning new pieces of this type but that can only exist in 3D boards or higher dimensional, with more than one area trajectories.

Someone at chessvariants.com pointed out that this idea has been used before, in the context of 3D variants. In particular, the piece called 'Base' in the 3D variant Prince moves exactly like the Pantheon in each of the three coordinate planes that contain it. Still, I am surprised this idea is not used more often in ordinary 2D variants. It seems a very useful intermediate between a normal slider and a hook mover. The latter are in general too strong to be useful.

Also interesting is that the value of these 'planular' moves should go up compared to ordinary slides and leaps as the board empties. This is exactly the opposite behavior as one has for hoppers, which become nearly useless if the board empties. Perhaps in a planular hopper the two density effects would cancel each other, and give it a more stable value.

Thanks HGMuller and Angel3D for clarifying the diagram - now I think I understand it. For a slight correction to the diagram above, if we assume all pawns are opponent pieces, the black lines indicate possible captures. But two more squares should be blue as possible move destinations. I added the blue (with orange stars to show the change). (Please reply if not correct).

I should create a chess variant for present this piece.
The idea of HGMuller about a "planular hopper piece" is also very interesting.