Truchet Tiles and Pattern

Like many items in our math as art section, complexity and the infinite emerge from simplicity repeated over and over again. In our Truchet tiles tool, we take one tile, give it two orientations, and place it in a pattern. The result is beautiful and surprising.

The History of Truchet Tiles

Truchet tiling traces back to 1704, with the work of Sébastien Truchet. A French priest and mathematician, Truchet became fascinated by the complexity possible in a simple pile of bicolored tiles, realizing that rotation alone could reveal numerous symmetrical permutations. On an interesting note, his work with tiles began with the observation of the French canals that he was commissioned to design. His work was later taken up by Pierre Fournier, who developed more complex shapes inspired by his work with word fonts (a passion that Truchet also shared).

Later still, Cyril Smith expanded the system to include curved, macaroni-like arcs. These are the building blocks of modern Truchet work. A metallurgist by trade, Smith used these tiles to model the hidden interfaces where crystals meet within a solid.

Smith’s system focused on the Critical Point, the “singularity” of the boundary, explaining the exact moment a structure shifts from one state to another. Today, we use these same patterns to visualize Bernoulli Percolation, demonstrating how a system of random, individual tiles can suddenly snap into a single, connected web. In our tool, we can see this when we select values that move away from random orientation. Entropy measures that residual order: even at maximum randomness, the underlying tile geometry constrains what the pattern can become.

An Explanation of Image

The tool offers several tile families: arc, diagonal, and quarter circle, each built from the same asymmetrical principle. Truchet tiles are asymmetrical by design; each one carries a curve connecting two of its four edges, but the curve never runs corner to corner symmetrically. When tiles sit next to each other, those curves either close into loops, circles when four tiles align just right, or irregular enclosed shapes when they don’t, or trail outward as open paths that wander to the edge of the grid without closing.

The bias slider governs which outcome dominates, not by changing the tile itself, but by shifting the probability that any given tile lands in one orientation rather than the other. At 50/50, the grid holds both in tension, producing a mix of enclosed rings and wandering lines. Push the slider toward either end, and one type wins, mostly circles or mostly open wandering paths, and the pattern becomes simpler.

From random placement of these tiles, recognizable forms emerge: quilt blocks, blobs, circles, and labyrinths, all from the same small set of rules. Just as with quilting, an enormous variety of patterns can be created by changing the symmetry settings. Even setting blobs, quilt blocks made of triangles alone, can produce a seemingly endless number of arrangements. Yet rules still operate beneath the surface; this is why random placement still looks ordered, it has a memory of the placement of other tiles.

How to Use Our Truchet Tiles Tool

Getting Started

Select a tile family from the top of the panel: triangle or arc. Click Randomize to generate your first pattern.

Tile Families

Arc tiles produce the characteristic Truchet curves and loops. Diagonal tiles create angular, quilt-like patterns from contrasting triangles. Quarter-circle tiles produce bold circular forms. 

Rotation States

Two states give the classic Truchet binary choice. Four states add more orientations and variety.

Grid and Geometry

Grid controls how many tiles across and down. Tile size controls the size of each tile. Stroke weight controls the thickness of the drawn lines. Bias controls the probability split between orientations; at 50/50, you get the richest mix of loops and open paths. Slide toward either end to favor one type.

Pattern Logic

Symmetry imposes a mirror or rotational constraint on the random placement. Quad and Rotational produce the most quilt-like results. Algorithm changes how tiles are initially assigned: Random is pure chance, Clustered groups similar orientations together, Wave introduces a flowing directional bias.

Color and Style

Choose a palette from the swatches. Fill style changes how the tile backgrounds are rendered — Two-tone is the traditional Truchet look, Paths colors each connected loop or line a distinct color.

Exporting

Save PNG exports the canvas as a flat image. 

Interactive Editing

Click any tile on the canvas to flip it forward one orientation. Right-click to flip it backward. Click and drag to paint flips across multiple tiles.