man atom4 (6): two-player color puzzle game

SYNOPSIS

atom4 [ -a n ] [ -d level ] [ -mt | -mx ]
atom4 -h

DESCRIPTION

Atom-4 is a two-player color manipulation game played with colored spherical pieces on a board divided into equilateral triangles. The player who first makes a row of 4 pieces of the right color wins.

There is an AI mode where you play against the computer. By default, atom4 runs in 2-player mode. Since 2-player mode is controlled from the same terminal, it can be used as a "practice" mode to acquiant oneself with the color change rules or to explore strategic possibilities in a controlled way.

atom4 supports both a curses-based text interface and an X11 interface. The interface can be selected with the -m option. By default, atom4 launches the X11 interface if the $DISPLAY environment variable is set, and the curses-based interface otherwise.

OPTIONS

-a n: Play against AI player. n must be either 1 or 2, specifying which player the AI will be.
-d n: Set AI player's difficulty level, where n is an integer from 0 or larger. The default difficulty setting is 2. This version of Atom-4 uses a real min-max algorithm; higher difficulty settings are actually much harder unlike in the previous version. However, be warned that very high difficulty settings will likely be very slow, as the game tree grows very quickly.
-h: Shows a summary of command-line options that atom4 takes.
-mt: Selects the text (curses-based) interface. The curses-based interface requires a terminal with color capabilities; at least 9 colors are needed.
-mx: Selects the X11 interface. The X11 interface requires an X display that supports at least 8-bit color. Note that currently, atom4 will always connect to the X server specified in the $DISPLAY environment variable.

TEXT MODE INTERFACE

The text mode interface requires a terminal that supports at least 9 colors.

The game controls are straightforward: the keypad arrow keys move the cursor around the board, and the Enter key or the Space key will place the piece being played on the board. The panel on the right shows you which piece is currently being played. Gameplay proceeds until one of the players win.

You can press q at any time to quit the game.

After one of the players win, the game will pause. You can either press n to proceed to the next round, or q to quit.

X11 INTERFACE

The X11 interface requires an X display which has at least 8-bit color.

Gameplay on the X11 interface is simple: the color wheel in the right panel shows the order in which pieces are played, as well as the current player (number in the center). The current piece being played is highlighted in the color wheel. To play the piece, simply locate your mouse over the desired spot on the board and click the mouse button.

When it is your turn to play, and your mouse hovers over a legal position where you can place a piece, the piece you are currently playing will appear under the mouse cursor. It is not actually placed on the board until you click the mouse button.

At any time during the game, you may press q to quit the game.

After one of the players win, press n to proceed to the next round.

GAME RULES

(Adapted from the README file.)

Pieces may be placed only on the vertices of the triangular game board divisions, and only if touching two other pieces which themselves are adjacent to each other (i.e., it must form an equilateral triangle with two adjacent pieces already on the board). Theoretically, the board is unlimited in size; practically, we limit it to 16 vertices across and 16 rows down.

Pieces have 8 different colors in total, grouped into 4 groups:

- black
- red, green, and blue (the primary, or "additive", colors)
- yellow, cyan, and purple (the secondary, or "subtractive", colors)
- white

Black and white are also called "propagators" (explained below).

The first player plays additive colors, and must make a row of 4 whites. White is the "goal piece" of the first player. Similarly, the second player plays subtractive colors, and must make a row of 4 blacks. Black is the "goal piece" of the second player.

Since neither player can play their goal pieces directly, they need to combine the colors they play in order to form their goal pieces on the game board, indirectly. Whenever an additive or subtractive piece is put on the board, it changes the color of pieces surrounding it. The color changes are illustrated by the following color wheel:

                      red   yellow
                         \ /
                 purple --*-- green
                         / \
                     blue   cyan

: 1) If the neighbouring piece has an adjacent color on the wheel, it does not change. For example, if red is placed next to yellow or purple, the yellow or purple remains the same.
: 2) If the neighbouring piece has a color 60 degrees away on the wheel, then it changes to the color in between. For example, if red is placed next to green, the green turns into a yellow. If a red is placed next to a blue, the blue turns purple.
: 3) If the neighbouring piece has the opposite color on the wheel, then it changes to either white or black, depending on what type of color the new piece is. If the new piece is an additive piece, the neighbour becomes white; if it is a subtractive piece, the neighbour becomes black. For example, if a red is placed next to a cyan, the cyan turns white; but if a cyan is placed next to the red, the red turns black.
: 4) If the new piece is additive and the neighbouring piece is black, then the black changes to the same color as the new piece. Similarly, if the new piece is subtractive and the neighbouring piece is white, then the white changes to the same color as the new piece.
: 5) If the new piece is additive and the neighbouring piece is white, then the white does not change, but the color change effect "propagates" through the white to the piece behind the white. That piece then changes as though the new piece had been placed next to it. If it is also white, then the effect continues propagating in the same direction, in a straight line, until it reaches a non-white piece, and then changes that non-white piece as though the new piece was placed next to it. If an empty spot is reached before a non-white piece, then nothing happens. Because of this effect, white pieces are also called "additive propagators".
: 6) Similarly, if the new piece is subtractive and the neighbouring piece is black, the color change effect propagates in the direction of the black until it reaches a non-black piece, which then changes as though the new piece had been placed next to it. Nothing happens if an empty spot is reached before a non-black piece. Hence, black pieces are also called "subtractive propagators".

(Another way to understand the color changes is treat colors as red, green, and blue combinations. Additive colors always try to "add" themselves to their neighbours: red + green = yellow (red & green together); red + cyan (green & blue) = white. Subtractive colors try to remove their complement color from their neighbours. For example, the complement of yellow (red & green) is blue; so yellow tries to remove blue from its neighbours. Hence, when yellow (red & green) is placed next to cyan (green & blue), the cyan turns green (loses the blue component). Similarly, when cyan (green & blue) is placed next to white (red & green & blue), it removes its complement, red, from the white; so the white becomes cyan as well. In other words, additive colors behave like colored light, whilst subtractive colors behave like colored paint.)

The initial state of the board consists of two pieces, green and purple, in the middle of the board, touching each other. The first player then plays a red, the second player plays a yellow, and then the first player plays a green, and so on, taking turns, going clockwise around the color wheel. The first person to make a row of 4 propagators wins.

If the game is played in multiple rounds, the second player may start first on the second round, using a subtractive piece, and then the first player with the next color clockwise on the color wheel, and so on. The starting configuration always consists of two pieces, one 30 degrees counterclockwise from the starting color on the color wheel, and the other 60 degrees clockwise; each touching the other in the center of the board.

GAME STRATEGY CONSIDERATIONS

Notice that in order to get from additive colors to white, the first player must form secondary colors and then add their complements; but the second player already plays secondary colors. So the first player can make use of the pieces played by the second player to make whites, which is faster than building whites from scratch. Similarly, the second player plays subtractive pieces and must first form primary colors and then add the complements to make black; but the first player already plays primary colors, which can be exploited to make blacks.

This also means that when playing a piece, one should be careful not to give too much advantage to the other player by providing material to make propagators (black or white).

Propagators (blacks or whites) are useful for changing colors of pieces already blocked from direct access because they are surrounded by other pieces. Using propagators, you can create more propagators from such "buried" pieces. Strategic positioning of propagators that allow you to reach these "internal" pieces is key to winning the game.

Since it is relatively easy for one's opponent to prevent one from winning by changing the color of a piece intended to be the 4th propagator in the row of 4, a good strategy is to devise a way to have at least two different pieces that can serve as a 4th piece in the row. Another good strategy is to bury the prospective 4th piece with other non-essential pieces so that the opponent cannot easily reach it, and have multiple propagator paths to it. Then if the opponent blocks one propagator path, another one is available to reach it.

It is very useful to anticipate the color of one's subsequent piece, and plan accordingly. For example, if the first player is playing a red, and there are no cyans around, it is useful to place the red next to blue pieces, because they form purple which can be complemented by the green on the next turn. If they are placed next to green pieces, the result is yellow, which cannot be used until 2 turns later.

HISTORY

The original 2-color version of the game was developed in December 2002. It was based on much simpler rules (basically, each player directly plays his goal piece), but because of the very small initial state space and the proximity of winning states, one player always had the advantage. Several different starting configurations, including randomized starting states, were tried in an attempt to balance the game, but with limited results.

Because of these limitations, more elaborate versions of the game were sought. The current 8-color version was first introduced in February 2003. Its main motivation was to postpone winning states until the state space has grown significantly.

A min-max algorithm with alpha/beta pruning was introduced to the AI player in April 2003. This replaced the previous, more limited algorithm which only performed well at certain search depths.

The "4" in the name "Atom-4" refers obviously to the goal of making the 4-in-a-row. The "atom" part refers to the similarity to atoms forming into a crystal lattice: you can't just stick an atom anywhere in a crystal lattice; it must fit into a "stable" position (in this case, touching two other adjacent "atoms" already on the board). Also, atoms don't just stick together; chemical reactions (color changes) happen when they come together, and some chemical changes have far-reaching effects (color change propagating over whites and blacks).

AUTHOR

The game concept of Atom-4, the design and implementation of the software version of the game, and the graphics used by the game, were all done by Hwei Sheng Teoh <[email protected]>.

COPYRIGHT

This is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2, or (at your option) any later version without ANY WARRANTIES.