Having a general template for ND spaces on how the pieces move is needed for the evolution of these games.

As well as some pieces are tricky in 3D chess in relation to 2D chess, 4D chess or 5D chess is challenging in relation to 3D chess

1. The dimensions

1D chess is a simple row of squares where only pieces like the rook, the dababba, pawns or grasshopper can move on. The only reason for the use of squares instead of lines is because there is need to 2D space for showing the pieces.

This has been submitted as a WoF 2 player game, this year.

2D chess is classical chess, that we all know, where pieces can move in two dimensions, with ability to combine directions, like the knight, bishop, king (instead of wazir) or queen (instead of rook).

3D-GrandChess has the same figures as conventional chess, but the pieces move differently, with the ability to move in the 3rd dimension, even if there cannot be made the combination of 3 dimensions in a single move. instead, they choose a 2D plane for each move (or a 1D line for the rook)

[Note: i will be using Japanese letters for the 4th dimen] The fourth dimension can refer to time, where pieces can move to the past, being unable to move for the rest of the game, and disappearing from next boards, or be treated in the fifth dimension as in a parallel universe. a fourth dimension can also be static, like our 3rd dimension, without referring to time, by considering an expanded cube, and treating the moves through dimensions as with a 2D chessboard compared to a 3D chess-framework. Or, by creating custom pieces with specific movements on the four dimensions. this system can go further and create squares of cubes, cubes of cubes, rows of cubecubes (7D), etc. until ∞D

2. Comparing dimensions - the directions

a piece can have a force of movement in a certain number of dimensions - the directions. a reduced number of dimensions may leave open the question on how a piece would move with more dimensions, because multiple options lead to the same in 2D, or sometimes, 3D.

Establishing the steps on each direction of a piece is important, or confusions may happen. The knight, for example can be thought of two ways:

1 - it moves 2 squares in one direction and then one square in another

2 - it moves in a diagonal step and then one orthogonal step respecting the diagonal direction (this is wrong)

both are fine in 3D and 2D, but if we go 4D, what does an orthogonal step mean? that means it keeps ONE 3d world.

1: あαa1 - うβa1 is possible

2: あαa1 - うβa1 is not possible

Time traveling method would be similar.

so defining how a piece moves in general should be made using directions.

3. Pieces movement

The rook moves any number of squares in one direction. [one square for wazir]

The bishop moves any number of squares, the same in two directions and never moving on a third one [one square for ferz]

The king combines wazir and ferz.

The knight moves 2 squares in one direction and then one square in another

The queen combines the rook and the bishop

The pawn moves in a 1D row and captures like a forward ferz

It is important to note that more dimensions give more opportunities to make more pieces, that move, by force, in 3D space.

3D-Chess

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