I03Available
Square Kolam Tile Challenge
Use all sixteen globally oriented tiles to build one connected nonzero kolam on a 4 × 4 board.
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Kolam Tiles
What global forms emerge when binary kolam tiles are assembled under local edge-matching rules?
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Tools & experiments
4 interactives
I04Available
Slide to a New Kolam
Move tiles through the open cell while preserving a correct square kolam, and watch the orbit invariant.
I05Available
Move X to Y
Transform one completed kolam into another and compare two configurations in the same 15-puzzle orbit.
I06Available
Kolams on an Octahedron
Compare three connected triangular kolam nets, fold each into an octahedron, and explore the completed solid.
The central question
What global forms emerge when binary kolam tiles are assembled under local edge-matching rules?
The square branch encodes the sixteen four-bit words as globally oriented tiles. Adjacent bits must match, the boundary must close, and the fifteen nonzero tiles must form one connected network.
Removing the 0000 tile produces a labelled 15-puzzle, bringing parity and orbit structure into the problem of moving between valid boards.
The triangular branch places the eight three-bit words on an octahedron; the dual cube converts the classification into a forced seven-vertex tree with three arm-length patterns.
KolamsCombinatoricsGraph theorySymmetry
Recent changes
The octahedron explorer and its graph-theoretic article joined the three square-tile sandboxes.
All interactives last tested 29 July 2026.