Truchet tiles in OpenSCAD

I’ve created an OpenSCAD script that generates Truchet tiles. Truchet tiles are square tiles decorated with patterns that are not rotationally symmetric. When placed in a square tiling of the plane, they can form varied patterns. The original Truchet tiles stem from a paper published in 1704 written by a french monk Sebastian Truchet. The Truchet tiles were popularized by Cyril Smith in a scientific publication in 1987.

The basic Truchet tile that I use here are two quarter-circles connecting the midpoints of adjacent sides. This tile can be rotated 90 degrees to result in a different tile.

Find below a bit of explanation about the OpenSCAD script but if you want a link to the OpenSCAD files and 3d printable files go straight to the bottom.

The script randomly generates a square of the tiles and produces interesting patterns. The center of the script is the tile module that (together with the tori module) creates a square cube and two tori. The tori are positioned in such a way that, when subtracted from the square, result in the tiles above.

module torus(r1,r2) {
    rotate_extrude(convexity=10,$fn=100)
    translate([r1,0,0])
    circle(r2,$fn=30);
}

module tile(size) {
//create a single tile
    difference() {
        h = 5; //height of a tile
        cube([size,size,h],center=true);
        translate([size/2,size/2,h/2]) torus(r1,r2);
        translate([-size/2,-size/2,h/2]) torus(r1,r2);
    }
}

The function rnd(n) ensures that the tiles are randomly rotated either 0 or 90 degree. The parameters size and mx are the size of the tile and the size of the square respectively.

function rnd(n) = (n>0.5) ? 90 : 0;

The rest of the script just loops in two dimensions to create a two-dimensional array of tiles. The size of the array is determined by the variable mx. See below an example of mx=60.

The end result can be used in something simple as a coaster or to decorate a vase. I expanded the original truchet script a little bit to create these 3d printer coasters.

I uploaded the end result to Printables and besides the .stl and .3mf files for the 3d printer I made the source code available both for the truchet tiles and the complete coaster: https://www.printables.com/model/1102980-truchet-tiled-surface-and-coaster.

Thanks for reading!