Named after Sebastien Truchet (1657 - 1729) who studied tiling of squares with a diagonal orientation.

2 Dimensions

POVRay source, tile on the x-y plane #declare RADIUS = 0.1; #declare oneunit = intersection { box { <0,0,-RADIUS-1>, <1,1,RADIUS+1> } union { torus { 0.5, RADIUS rotate <90,0,0> } torus { 0.5, RADIUS rotate <90,0,0> translate <1,1,0> } } translate <-0.5,-0.5,0> }

2x2 tilings

Each unit is randomly rotated by 0 or 90 degrees or flipped vertically or horizontally, there are only two unit states.

5x5 tilings

Larger tiling [POVRay source]

3 Dimensions

POVRay source #declare RADIUS = 0.1; #declare oneunit = intersection { box { <0,0,0>, <1,1,1> } union { torus { 1/2, RADIUS rotate <90,0,0> translate <0,1,1/2> } torus { 1/2, RADIUS rotate <0,0,90> translate <1/2,0,1> } torus { 1/2, RADIUS translate <1,1/2,0> } } translate <-1/2,-1/2,-1/2> }

2x2 tilings

Each unit is randomly rotated by integer multiples of 90 degrees about each axis and randomly mirrored about each cartesian axis plane (xy, xz, yz).

3x3x3 tilings

Larger tiling [POVRay source]

Contribution by Robert McGrego

Contribution by Robert McGrego

2D tiling ... actually an orthographic projection of a 3D model

Perspective from the same position as above

Perspective projection from another position

POVRay scene file: blocktile.pov

Single tiling unit (Unit square in red).

Perspective view of single tiling unit.

Regular tiling.

Randomised tiling.

Perspective view of the randomised tiling.

POVRay scene file: weave.pov for the single unit.
Scene file for a random tiling of the plane: weave.pov.