FloaTiles — off-lattice particle model

Rigid Hat monotiles floating on a shallow pool, pulled together by the capillary (Cheerios) force along their rims and stirred by a surface circulation. The tiles are the exact Tile(1, √3) outline at the printed size, and contacts, friction and walls are handled by a rigid-body solver compiled to WebAssembly. The default circulation is the one fitted to the real pool with a fan blowing across it. ← back to project page

What you are looking at. Each tile is one rigid body built from the exact Hat outline, cut into five convex pieces for the contact solver. Every element of a tile's rim is attracted to the nearest rim of a neighbour with line energy e_b dl exp(−gap/l_c), where l_c is the capillary length of the liquid, 2.73 mm. Because the force acts along the rim rather than between centres, two tiles whose long edges face each other rotate until they are flush and then bond along the whole edge. No bond is ever stored and there is no break-up rule: clusters come apart when drag, shear or an impact beats attraction plus friction. Tiles are dragged toward a surface flow, and the agitation slider adds a per-tile random force standing in for a vibrating table.

Things to try. Let it condense at the default settings, then push the agitation up: tiles unpin from the shapes friction had frozen them into, and the clusters tighten. Drop the bond energy to zero and the aggregate disperses. Switch the rim bond off, which replaces the edge-aware attraction with a plain centre-to-centre pull — tiles then clump without aligning, and you can see the difference the tile's geometry makes.

What this is and is not. The physics is the working model, not a cartoon of it: the same capillary kernel, the same drag law, the same contact treatment, and by default the same fan-driven circulation, obtained by fitting a wind-stress model of the fan to the flow measured in the pool. What differs from a research run: the tiles start from a random layout rather than a recorded one, the tile count is kept below the experiment's so the page stays interactive, and the random numbers and the contact solver are not the ones used in Python, so runs will not match trajectory for trajectory. It is an instrument for intuition rather than a source of numbers, and no result from the ongoing analysis is shown or implied.

Contacts and friction: Box2D v3 (Erin Catto) through box2d3-wasm, falling back to Rapier (Dimforge) if that cannot load. The model this is ported from is written in Python over Pymunk (Victor Blomqvist), which wraps Chipmunk2D (Scott Lembcke). The Hat monotile is from Smith, Myers, Kaplan & Goodman-Strauss, An aperiodic monotile (arXiv:2303.10798, 2023).