Colorfield is played on an even sided, rectangular grid of dots, outlining unit squares. Two players, Red and Blue, take turns drawing unit length segments of their own color, one segment per turn, starting with Red. Passing is not allowed, but if you don't have an available move, your turn is skipped. Colorfield uses the pie rule: Blue, on his first turn, has the option of switching colors and becoming Red, taking the first segment as his own, instead of drawing a blue segment.
A region is a set of one or more squares connected through shared sides. The bordering segments of a region are the sides of its squares, leaving out the sides shared by two of its squares. When all of the bordering segments of a region are drawn, the region is enclosed and is owned by whoever has more bordering segments, and it is colored in the owner's color. You must not enclose a region with an equal number of red and blue bordering segments, and you must not subdivide an already enclosed region. Illegal segments are marked with black dotted lines.
Whoever owns the majority of the squares wins, and the game ends at that moment.
3D Colorfield is played on a 4x4x2 or 6x6x2 grid of dots, outlining unit cubes. The grid is drawn as a front grid and a back grid, with the segments between them drawn diagonally. A volume is a set of one or more cubes connected through shared faces. The bordering segments of a volume are the edges of its cubes, leaving out the edges of faces shared by two of its cubes. When all of the bordering segments of a volume are drawn, the volume is enclosed.
Your segment may complete the enclosure of several intersecting volumes at once. The total volume your segment encloses is the union of them, and it includes only cubes that are not part of an already enclosed volume. The total enclosed volume is owned by whoever has more bordering segments, and it is colored in the owner's color; where a red and a blue cube overlap in the drawing, the overlap is purple. If your segment completes the enclosure of two volumes that share no cube, both are enclosed, each with its own owner.
The total volume your segment encloses must not have an equal number of red and blue bordering segments. Unlike in 2D, an enclosed volume can be subdivided: segments can be drawn inside and around an already enclosed volume, and the whole volume keeps its original owner and color. Whoever owns the majority of the cubes wins, and the game ends at that moment.
4D Colorfield is played on a 4x4x2x2 grid of dots, outlining nine unit hypercubes. The grid is shown as two 3D boards, Board 1 and Board 2, which together form one 4D board. A segment between the two boards is called a connector. It is shown as a colored dot in the same place on both boards. On your turn, draw a segment of your color on either board, or form a connector by tapping a dot, which draws a dot of your color in the same place on each of the two boards.
A unit is made up of a cube on Board 1, the cube in the same place on Board 2, and the eight connectors between their corners: 32 edges in all, 12 on each board and 8 connectors. Volumes, enclosing, owning and legal moves are exactly as in 3D, with connectors counting as bordering segments like any other segments. An enclosed unit is colored on both boards. Whoever owns five or more of the nine units wins.
About this app. Level 1 plays at random. Levels 2 to 6 play a Monte Carlo tree search of increasing depth, at most three seconds a move (five at level 6), levels 3 to 6 thinking on while you think, levels 4 to 6 with an exact search of the endgame; the hint uses the level 4 search. The last move is marked with yellow dots: two on a segment, one in a connector. On the menu, each color can be a human or a computer level, so you can play either color, play another person, or set both colors to the computer and watch the game play out. A game in progress is kept in the browser and can be resumed from the menu. Record shows the moves of the game as text, to copy or print.