# CONTINUOUS CHESS

- The board is a single 8"x8" square.
- Each piece is a circle with a 0.5" diameter.
- The position of a piece is the location of the center of the piece's circle.
- The extent of a piece is the circular area which the piece occupies.

## Initial piece positions [x, y]

White | Black |
---|---|

Rook starts at [0.5", 0.5"]
Knight starts at [1.5", 0.5"] Bishop starts at [2.5", 0.5"] Queen starts at [3.5", 0.5"] King starts at [4.5", 0.5"] Bishop starts at [5.5", 0.5"] Knight starts at [6.5", 0.5"] Rook starts at [7.5", 0.5"] pawns starts at |
Rook starts at [0.5", 7.5"]
Knight starts at [1.5", 7.5"] Bishop starts at [2.5", 7.5"] Queen starts at [3.5", 7.5"] King starts at [4.5", 7.5"] Bishop starts at [5.5", 7.5"] Knight starts at [6.5", 7.5"] Rook starts at [7.5", 7.5"] pawns start at |

The above diagram is a scaled down model of the board with initial array.

## Movement

- King moves 0, 90, 180, or 270 degrees, up to a distance of 1.0"
- King moves 45, 135, 225, or 315 degrees, up to a distance of sqrt(2)"
- Queen moves 0, 45, 90, 135, 180, 225, 270, or 315 degrees, any distance
- Rook moves 0, 90, 180, or 270 degrees, any distance
- Bishop moves 45, 135, 225 or 315 degrees, any distance
- Knight leaps with a bearing of arctan(0.5), arctan(2), arctan(-0.5) or arctan(-2) up to a distance of sqrt(5)"
- pawn moves (non-capturing) 90 degrees up to a distance of 1.0"
- pawn captures 45 or 135 degrees up to a distance of sqrt(2)"

sqrt(n) is shorthand for the square root of n.

arctan(0.5) = (approx.) 26.565 or 206.565 degrees.

arctan(2) = 63.435 or 243.435 degrees.

arctan(-0.5) = 153.435 or 333.435 degrees.

arctan(-2) = 116.565 or 296.565 degrees.

0 degrees would be movement directly to the player's right, with 90 degress being movement directly forward.

The x or y position of a piece may never exceed 8, nor may it be less than zero.

Pieces must cease movement when their extent overlaps the center point of another piece. Since Knights leap, this limitation does not apply to Knight movement.

Friendly pieces cannot ever overlap their extent with another friendly piece's center point. This limitation does not apply to a Knight while it is moving, but does apply to the Knight when it stops moving.

Castling and en passant are not allowed.

Pawns may make an initial non-capturing move of up to 2.0" (90 degrees).

Players should not be allowed to make moves of a distance less than N, where N is of some 'significant' distance (eg. 0.1"). This would prevent players from making what amounts to NULL moves.

## Pawn Promotion

White pawns promote when their extent overlaps a point at y position 7.5.Black pawns promote when their extent overlaps a point at y position 0.5.

## Capture

A capture occurs when a piece moves to a location such that its extent (circular area) overlaps the center point of an opponent's piece! Movement must stop when the first overlap of an enemy piece's center point occurs, except for the Knight, which leaps.As a reader pointed out, a piece may end up capturing more than one piece with a single move. By my calculations (which should be taken with a large grain of salt), the Knight can capture up to five pieces at once, while the other types of pieces can capture up to three pieces.

## Check

The King is now a 'ranged' piece, and so is not allowed to move through check.## Notes

Inches are used in this document, although any unit of distance could be used instead.It is impractical to attempt to play this game on a physical board with physical pieces. Ideally it would be played using a computer with a Graphical User Interface. Since visualizing moves would be extremely difficult, the computer program would have to show the user the possible movement paths of each piece.

The potential for variants of this game are enormous -- pieces of different shapes and sizes, elongated pieces, pieces which move along various curves, three dimensional movement, playing on various curved sufaces, etc.

## Some different piece ideas

Guard: Leaps to any point within a 0.5" circle radius.Sword: Instead of being a circle, it's an isosceles triangle with a base of 0.2" and a height of 1". It's center point is at the midpoint of its bisecting line. The Sword can only move in the direction of its bisecting line. If it moves 'backwards' it cannot capture. It may also rotate on its center point any number of degrees, between, but not including zero and 360 degrees.

Flea: A 0.1" radius piece. It leaps 45, 135, 225 or 315 degrees, any distance, but can only land at 0.5" intervals.

## Zeno Continuous Chess

As above, except the maximum distance a piece can move is half the distance from the piece's center point to the edge of the board (in the direction that it is moving in).With the above rule, no piece may ever achieve an x or y position of 0 or 8.

## Discrete Continuous Chess

Continuous Chess, except that the distance pieces can move must be a multiple of some specific distance (for example 0.5").Written by David Howe. Thanks to Peter Aronson, Jim Aikin, Mark Thompson, A.J. Winkelspecht and 'Gnohmon' for their comments, suggestions and corrections.

WWW page created: 16 May 2001. Modified: 21 May 2001.