Why do the arcs always connect even though each tile is random?

Every tile's arc, in either orientation, always touches the midpoint of all four of its edges — so any two neighbors are geometrically guaranteed to connect.

No — it's a pure local computation.

Yes — free, no download, in your browser.

Where do Truchet tiles come from?

They're named after Sébastien Truchet, a 17th-century French mathematician who first studied the patterns made by tiles like these.

Why do the arcs never end in the middle of a tile?

Each arc runs between the midpoints of two edges, and every tile has the same midpoints, so any arc always continues smoothly into the neighbouring tile.

Do the curves form closed loops?

Yes, many do, at all sizes, and others wander far across the grid. The mix of small loops and long paths is typical of random Truchet patterns.

Is it related to any maths beyond art?

Yes. The connectivity of random Truchet tilings can be analysed as bond percolation at the critical point, studied in statistical physics.

Truchet Tiles Screensaver

Truchet tiles are square tiles, each holding a quarter-circle arc, that can be placed in one of two random real orientations. Laid out across a grid with no coordination between tiles, the arcs still always line up edge to edge — producing a continuous, ever-shifting maze-like weave purely from independent random choices.

How the Truchet Tiles screensaver works

Each square tile carries one real quarter-circle arc, drawn corner to corner across the square.

Every tile independently and randomly picks one of two mirrored orientations for its arc — there is no coordination between neighboring tiles at all.

Because every tile's arc always touches the midpoint of each of its four edges, any two neighboring tiles' arcs always connect smoothly, regardless of their independent random choices.

The result is a continuous, snake-like maze of curves that emerges purely from independent per-tile randomness, slowly reshuffling as new tiles are laid.

From a priest's tile patterns to percolation

Sébastien Truchet was a French priest and scientist who, in 1704, published a memoir on combinations of tiles: patterns made from a single square tile divided along a diagonal into two colours. Rotating the tile in four ways gave a surprising variety of designs. The quarter-circle version used in this screensaver was popularised much later, in a 1987 article by the metallurgist Cyril Stanley Smith.

Smith's version draws two quarter-circle arcs on each tile, each joining the midpoints of two adjacent edges, and each tile is placed in one of two orientations. Every arc ends at the middle of an edge, so it always meets the arc of the neighbouring tile, however the orientations are chosen. The picture is therefore a set of continuous curves, some forming closed loops and others winding for a long way across the grid.

The pattern is more than decoration. The connectivity of such tilings can be analysed as bond percolation at its critical point, a standard topic in statistical physics. That explains the look of the display: it is neither regular nor chaotic, with loops of every size appearing together.

A worked example

Watch a fresh wave of tiles sweep across the grid, each one independently rolling its own orientation — yet the curves it draws always connect smoothly into its neighbors, weaving a continuous path with no gaps or mismatches anywhere.

Settings & tips

Line color recolours the drawn arcs.
Tile size trades finer detail for a bolder, chunkier weave.
The grid reshuffles with a fresh random layout every so often.

Frequently asked questions

Why do the arcs always connect even though each tile is random?: Every tile's arc, in either orientation, always touches the midpoint of all four of its edges — so any two neighbors are geometrically guaranteed to connect.
Is a key needed?: No — it's a pure local computation.
Is it free?: Yes — free, no download, in your browser.
Where do Truchet tiles come from?: They're named after Sébastien Truchet, a 17th-century French mathematician who first studied the patterns made by tiles like these.
Why do the arcs never end in the middle of a tile?: Each arc runs between the midpoints of two edges, and every tile has the same midpoints, so any arc always continues smoothly into the neighbouring tile.
Do the curves form closed loops?: Yes, many do, at all sizes, and others wander far across the grid. The mix of small loops and long paths is typical of random Truchet patterns.
Is it related to any maths beyond art?: Yes. The connectivity of random Truchet tilings can be analysed as bond percolation at the critical point, studied in statistical physics.

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