Technique · Fields
Truchet tiles
Square tiles with quarter-circle arcs, each turning by a quarter at its own random times, so winding paths and loops keep re-routing.
Truchet tiles is a field drawn for every pixel by the graphics chip. Every piece on Synapse Drip is made from a recipe that layers techniques like this one, and you can change any of it in the Studio.
Good to know
- In a random Truchet tiling with equal chances for each turning, the paths are the outlines of clusters at the critical point of percolation, a fractal with dimension 7/4.
- Tile design builds a rich wall from few modules: the zellige of Morocco and the azulejos of Portugal both use a small set of tiles whose edges match.
- In 2018 Christopher Carlson described multi-scale Truchet patterns, in which a tile is replaced by four smaller ones, giving the mixed-scale look of some modern graphics.
- Sebastien Truchet, a French priest and scientist, published his study of square tiles split into two colours in 1704; the arc version used here is usually credited to the metallurgist Cyril Stanley Smith, who studied it in 1987.
- A single line of the Commodore 64 language BASIC, printing one of two diagonal characters at random in an endless loop, became famous in 1982 as a maze maker: it is a Truchet tiling.
The mathematics
- With about 245 tiles in view, each set one of two ways, there are two to that power possible pictures; the paths never cross or break because every arc ends on a tile edge at a point it shares with the neighbouring tile.
- A single arc has radius one half of a tile and is centred on a corner, so it leaves every edge at its midpoint, and the line that leaves one tile is continued, whichever way the next tile is set.
- Every path is either a closed loop or runs off the picture, and the loops come in all sizes; the same kind of statistics, called percolation, are used to model how a fluid seeps through a porous stone.
In art
- Because every tile matches every other, the pattern looks designed whether it is random or not, which is why Truchet-style layouts are common in posters, wallpaper and video-game mazes.
- The one-line maze program of the early 1980s, 10 PRINT, and the whole book written about it in 2013, treat this single idea as a small artistic form.
More ways to use it
Related techniques
Nebula and stars · Liquid · Droplets · Network · Terrain and maps · Neuron · Order to chaos · Fractal tree