Truchet Tiling

Author

Eric W. Weisstein
December 11, 2002

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Tilings/TruchetTiling.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/TruchetTiling.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

<<Graphics`Colors`

Original Tile

Truchet[1,x_]:=Polygon[x+#&/@{{0,0},{0,1},{1,0}}]
Truchet[2,x_]:=Polygon[x+#&/@{{0,0},{0,1},{1,1}}]
Truchet[3,x_]:=Polygon[x+#&/@{{0,1},{1,1},{1,0}}]
Truchet[4,x_]:=Polygon[x+#&/@{{0,0},{1,1},{1,0}}]

Show[GraphicsArray[Table[Graphics[{
Truchet[n,{0,0}],
Line[{{0,0},{1,0},{1,1},{0,1},{0,0}}]
},AspectRatio->Automatic],{n,4}]]]

t=Table[Truchet[Random[Integer,{1,4}],{x,y}],{x,20},{y,20}];
Show[Graphics[t,AspectRatio->Automatic]]

Modified Tile

Truchet[0,x_]:={Circle[x,.5,{0,Pi/2}],
Circle[x+1,.5,{Pi,3Pi/2}]}
Truchet[1,x_]:={Circle[x+{0,1},.5,{3Pi/2,2Pi}],
Circle[x+{1,0},.5,{Pi/2,Pi}]}

Show[Graphics[{
{Red,Thickness[.02],Truchet[0,{0,0}]},
Line[{{0,0},{1,0},{1,1},{0,1},{0,0}}]
}
],AspectRatio->Automatic]

Tiling

t=Table[Truchet[Random[Integer],{x,y}],{x,20},{y,20}];
Show[Graphics[t,AspectRatio->Automatic]]