Truchet Tiles
Quarter-arc tiles re-rolling, one at a time, into a single continuous meander.
About this piece
Every cell of this grid carries the same tile: two quarter circles of radius half a cell, centred on opposite corners. Only the tile’s rotation differs from cell to cell — and because a 180° turn maps the tile onto itself, there are only two distinct orientations. One bit per cell decides the whole picture.
The reason it does not look like a grid of tiles is a single geometric fact: an arc of that radius, centred on a corner, begins and ends exactly at the midpoint of an edge. Its neighbour’s arcs land on the same midpoints, whichever way that neighbour is turned. So the joins are always seamless, and curves wander across the entire frame even though no cell knows anything about the cells around it.
Sébastien Truchet catalogued the patterns from a single rotatable square tile in a 1704 memoir for the French Academy; the quarter-arc version drawn here is the one Cyril Stanley Smith reintroduced to designers in 1987.
What to look for
About seven cells a second re-roll their target rotation, and each one eases into the new angle over roughly a second rather than snapping. Pick a long meander and watch it get cut and re-routed as a cell somewhere along it turns.
Roughly one cell in seven is coral. Colour belongs to the tile, not to the curve — so a single continuous loop will often change ink halfway round, which is a good way to see that the curves really are an accident of the tiling.
Honest limit: this is a grid, and the piece needs width to read. In a narrow phone-portrait frame you get about six cells across, and at that size it looks more like a pattern swatch than a meander. It is at its best wide.
Curious how the loop and canvas fit together? Read how it works →