Turn one tile.
Two loops become one.
Two little curves, repeated 36 times. Turn the marked square and watch two separate circles join. The pattern changes its connections, without using any more ink.
inside the square
touch the edge
same amount of ink
Four arcs each.
Follow the two white circles through the marked tile. That square belongs to both of them.
Tap any square to turn it. Keyboard: Tab into the board, arrow keys to move, Enter or Space to turn.
A local move can change the whole route. Try the marked tile above, then make a pattern of your own.
Follow the whole line.
Every arc belongs to exactly one route. Select a route below, or switch to Trace and choose a square. A route can travel far beyond the tile you touched.
The example highlights two separate 4-arc loops.
Showing the four longest closed loops and the two longest open paths. Counts describe this bounded square, not an infinite wallpaper.
Make a repeat worth keeping.
One square becomes a wall. Every line reaches an edge at its midpoint, so neighboring copies meet, whatever turns you make.
3 × 3 repeat. The dashed square marks one full board. Open paths continue into neighboring copies; the board's loop count does not describe this whole wall.
Changing size starts a fresh checkerboard.
Weight changes the drawing, not its connections.
Clean cyan artwork, without grid or highlights. Vector files with explicit colors and no external assets. Your edits live only in this tab; download before leaving.
One rule makes it seamless.
Keep the endpoints. Change who connects to whom. These are the two orientations of the quarter-circle tile popularized by Cyril Stanley Smith's 1987 study of Truchet patterns. Each edge has one midpoint connection. A turn swaps the pairings, while keeping both arc lengths and all four endpoints in place.
Sources and how the counts work
- Christopher Carlson, Multi-Scale Truchet Patterns, Bridges 2018: describes Smith's quarter-circle motif. This page uses equal-size tiles only.
- Robert Krawczyk, Infinitely Variable Tiling Patterns, 2020: original-author design and historical context.
- W3C, SVG 2 pattern specification: the exported wall uses a repeating pattern with explicit user-space dimensions.
- Original code and computed geometry, no external dataset. Each tile contributes two quarter-circle arcs of radius half a tile. Arcs connect across shared edges. A connected route with no endpoints on the outer boundary is a closed loop. Every other route has two boundary endpoints. For an N × N board there are 4N boundary endpoints, hence exactly 2N open paths, whatever the arrangement.
- A 6 × 6 board has 72 arcs and total centerline length 18π tile widths. The highlighted example merges two 4-arc loops into one 8-arc loop, reducing the closed-loop total from 13 to 12. It is a specific example, not a claim that every turn merges loops. Other turns can split a loop or reconnect open paths.
- Downloads retain the current board, line weight and fixed cyan/ink palette. The repeat tile is 600 × 600 units; the wall is 1800 × 1800, with nine copies. Highlights and boundary counting are inspection aids and are not exported. Sources checked 24 October 2026.