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Game Description

Breakthrough is an abstract strategy board game invented by Dan Troyka in 2000. It won the 2001 8x8 Game Design Competition.

Moves.The players alternate, with each player moving one piece per turn. A piece may move one space straight or diagonally forward if the target square is empty. A piece may move into a square containing an opponent's piece only if that square is one step diagonally forward. The opponent's piece is removed and the player's piece replaces it. Capturing is not compulsory, nor is it chained as in checkers.

Objective.The first player to reach the opponent's home row – the one farthest from the player – is the winner. If all the pieces of a player are captured, that player loses. A draw is impossible.

Board size. Change it on top and play different strategies!

Checkers or English Draughts, also called American checkers or straight checkers, are a form of draughts board game. Unlike international draughts, it is played on an eight by eight squared board (with sixty-four total squares) with twelve pieces on each side.

Moves. A simple move involves sliding a piece one space diagonally forwards to an adjacent unoccupied dark square. A jump is a move from a square diagonally adjacent to one of the opponent's pieces to an empty square immediately and directly on the opposite side of the opponent's square, thus jumping directly over the square containing the opponent's piece. An uncrowned piece may only jump diagonally forwards, kings may jump diagonally backwards. A piece that is jumped is captured and removed from the board. Multiple-jump moves are possible if when the jumping piece lands, there is another immediate piece that can be jumped; even if the jump is in a different direction. Jumping is mandatory – whenever a player has the option to jump, she must jump. When multiple-option jumping moves are available, whether with the one piece in different directions or multiple pieces that can make various jumping moves, the player may choose which piece to jump with and which jumping option or sequence of jumps to make. The jumping sequence chosen does not necessarily have to be the one that would have resulted in the most captures; however, one must make all available captures in the chosen sequence.

Kings. If a player's piece moves into the kings row on the opposing player's side of the board, that piece is said to be crowned (or often kinged in the U.S.), becoming a king and gaining the ability to move both forwards and backwards. If a player's piece jumps into the kings row, the current move terminates; having just been crowned, the piece cannot continue on by jumping back out (as in a multiple jump), until the next move. Any piece, whether it is a king or not, can jump a king.

Objective. A player wins by capturing all of the opposing player's pieces or by leaving the opposing player with no legal moves. The game ends in a draw, if neither side can force a win.

Board size. Change it on top and play different strategies!

Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. Each player begins the game with sixteen pieces: One king, one queen, two rooks, two knights, two bishops, and eight pawns. Pieces move in different assigned ways according to their type, and accordingly are used to attack and capture the opponent's pieces. The object of the game is to checkmate the opponent's king.

Moves. The moves differ by figure. Please consult the chess link above for a complete explanation with examples.

  • The king moves one square in any direction. The king has also a special move which is called castling and involves moving two fields towards a rook which has not moved before.
  • The rook can move any number of squares along any rank or file, but may not leap over other pieces. Along with the king, the rook, during the king's castling move, jumps over the king.
  • The bishop can move any number of squares diagonally, but may not leap over other pieces.
  • The queen combines the power of the rook and bishop and can move any number of squares along rank, file, or diagonal, but it may not leap over other pieces.
  • The knight moves to any of the closest squares that are not on the same rank, file, or diagonal, thus the move forms an L-shape two squares long and one square wide. The knight is the only piece that can leap over other pieces.
  • The pawn may move forward to the unoccupied square immediately in front of it on the same file; or on its first move it may advance two squares along the same file provided both squares are unoccupied; or it may move to a square occupied by an opponent's piece which is diagonally in front of it on an adjacent file, capturing that piece. The pawn has two special moves: the en passant capture and pawn promotion. In the first it captures another pawn which has just made a two-field move, in the other one it becomes a queen in the last row.

Objective. When a king is under immediate attack by one or more of the opponent's pieces, it is said to be in check. A response to a check is a legal move if it results in a position where the king is no longer under direct attack (that is, not in check). This can involve capturing the checking piece; interposing a piece between the checking piece and the king (which is possible only if the attacking piece is a queen, rook, or bishop and there is a square between it and the king); or moving the king to a square where it is not under attack. Castling is not a permissible response to a check. It is illegal for a player to make a move that would put or leave his own king in check. The objective of the game is to checkmate the opponent; this occurs when the opponent's king is in check, and there is no legal way to remove it from attack.

Connect4 (also known as Captain's Mistress, Four Up, Plot Four, Find Four, Four in a Row, and Four in a Line) is a two-player game played on a standing grid.

Moves. The players take turns dropping their colored discs from the top into a seven-column, six-row grid. The pieces fall straight down, occupying the next available space within the column, so to make a move click on a field which is empty and on top of a non-empty one, or in the bottom row.

Objective. The objective of the game is to connect four of one's own discs of the same color next to each other vertically, horizontally, or diagonally before the opponent can do so.

Board size. Change it on top and play different strategies!

Entanglement is a cops vs. robber game played on a graph, which plays an important role in structural theory of directed graphs.

Moves. The players move in turn. In each move the cops either stay where they are, or place one of them on the vertex currently occupied by the robber. The robber must move from her current vertex, along an edge, to a successor that is not occupied by a cop. The robber must move even if no cop is following him.

Objective. If there is no free successor to which the robber can move, she is caught, and the cops win. The robber wins if she cannot be caught and the cops give up.

Gomoku is an abstract strategy board game and is also called Five in a Row. The name Gomoku is from the Japanese language, in which it is referred to as gomokunarabe Go means five, moku is a counter word for pieces and narabe means line-up. The game is also popular in Korea, where it is called omok.

Moves. Players alternate in placing a cross or a circle on an empty square, starting from an empty 8×8 board.

Objective. The winner is the first player to get an unbroken row of five stones horizontally, vertically, or diagonally.

Board size. Change it on top and play different strategies!

Pawns is a training game for chess players. The aim is to improve one's handling of pawn play by concentrating solely on this aspect of chess.

Moves. The standard Chess pawn moves apply. Normally a pawn moves by advancing a single square, but the first time each pawn is moved from its initial position, it has the option to advance two squares. Pawns may not use the initial two-square advance to jump over an occupied square, or to capture. Any piece directly in front of a pawn, friend or foe, blocks its advance. A pawn captures diagonally, one square forward and to the left or right. Additionally, it may capture en passant. This arises when a pawn uses its initial-move option to advance two squares instead of one, and in so doing passes over a square that is attacked by an enemy pawn. That enemy pawn, which would have been able to capture the moving pawn had it advanced only one square, is entitled to capture the moving pawn in passing, as if it had advanced only one square.

Objective. The goal in Pawns is simply to be the first to bring one of the pawns to the other end of the board. Naturally, you also win if you capture the last pawn of your opponent. If all your pawns are blocked and you cannot move when you are supposed to, you lose.

Board size. Change it on top and play different strategies!

Tic-Tac-Toe also rendered wick wack woe (in some Asian countries), or noughts and crosses/Xs and Os as it is known in the UK, Australia and New Zealand, is a pencil-and-paper game for two players, X and O, who take turns marking the spaces in a 3×3 grid.

Moves. Players alternate in placing a cross or a circle on an empty square.

Objective. The player who first succeeds in placing three respective marks in a horizontal, vertical, or diagonal row wins the game.

Board size. Change it on top and play different strategies!

Hnefatafl is a strategic board game of the Vikings. There are many variations, but the most popular modern one is played on an 11×11 grid.

Warning! The game is incomplete and very slow for now!

Moves. Players move on free straight lines, vertical or horizontal.

Capturing Pawns. All pieces except the king are captured if they are sandwiched between two enemy pieces, or between an enemy piece and a hostile square, along a column or a row. A piece is only captured if the trap is closed by a move of the opponent, and it is thus allowed to move in between two enemy pieces. The king may take part in captures.

Capturing the King The king himself is captured like all other pieces, except when he is standing on the throne or on one of the four squares next to the throne. When the king is standing on the throne, the attackers must surround him in all four cardinal points. When he is on a square next to the throne, the attackers must occupy all surrounding squares in the four points of the compass except the throne.

Objective. The objective for the king's side is to move the king to any of the four corner squares. In that case, the king has escaped and his side wins. The attackers win if they can capture the king before he escapes.

Rewriting Example is the basic example we use to illustrate the way discrete structure rewriting works.

Bounce is the basic example we use to illustrate how continuous dynamics and invariants work with structure rewriting.

Yeast Cell Cycle model by Tyson (1991), described here, is a model of the cell cycle based on the interactions between cdc2 and cyclin. We use it as an example of non-linear dynamics with universal rules and parameters.

Parsing is a basic example to illustrate how parsing with type reconstruction can be represented as structure rewriting.

Forces can be represented using continuous dynamics, and in this example we show how to use them for graph drawing.