Tesseract Is Live: Play Four-Dimensional Chess

Tesseract is live: 4D chess, online, free, in a browser tab. The board is a 5×5×5×5 lattice — 625 cells — and we draw it as a 5×5 grid of ordinary 5×5 chessboards. That layout is the whole trick. Because the mapping is affine in all four coordinates, a straight line through four dimensions stays a straight line across the grid on your screen, so when you select a piece the highlighted cells march off in visibly straight rows, even the ones that cross four sub-boards at once. Straightness is how your eye learns a geometry it has never had to hold before.

Everything else is chess as you know it. Kings, rooks, bishops, knights, queens; check, checkmate, stalemate, castling, en passant, promotion. Four dimensions add two new sliding pieces — the unicorn and the dragon, which take the diagonals that only exist off a flat board — and two species of pawn, because a pawn needs a forward direction and there are now two spare axes for it to face. You can read all of that on the board in about ten minutes. Playing it well takes considerably longer.

There are five ways in:

• Play the engine at four strengths, from an instant opponent that answers in 60 ms to a master tier that thinks for up to 3.5 seconds and searches six plies deep. It runs in a Web Worker, so the page never freezes while it thinks.
• Two players, one screen — hotseat, the way chess variants have always actually been played.
• A guided tutorial of eight lessons, one piece at a time. Every lesson is proved winnable before it ships: the build plays every legal move of the lesson's piece through the real engine, and fails if a lesson can be failed.
• A pack of twelve puzzles, hand-built mate-in-N studies. None of them ship on our word — each has to pass a machine check for a solution that is exact, unique and forced.
• Play a friend online. One of you opens a room, the other joins it, and both clients re-check every move against their own rules engine rather than trusting the wire.

Two small things that are easy to miss. There is a hint button, backed by its own half-second search, and using it costs you nothing but pride. And there is a second view that drops the grid and draws the actual tesseract — the inner cube is one end of the fourth axis, the outer cube is the other — turning slowly through a rotation that has no analogue in three dimensions. It is useless for playing and very good for understanding, which is a fair description of most four-dimensional intuition.

It runs on phones and it works on a laptop trackpad, but four dimensions genuinely reward a large screen — twenty-five boards is a lot to hold at once. You can play the whole game from the keyboard if you prefer. Sound is off in one click, and that click mutes the rest of the Lab too, because there is exactly one mute switch across all thirteen games.

How it was built — the 80 attack directions, the mailbox that makes a 4D board fast, the 11.66-million-node perft count, the security model behind online play — is a separate and much longer piece: Chess in Four Dimensions.

The board is waiting: vaynerov.com/games/tesseract.