Ammann Tilings

Needs["AmmannTiling`"]

<< Graphics`Colors`

Ammann A5 (rhombs and squares)

There are two basic geometric objects: squareTile and rhombTile.

GraphicsArray[colorGraph[deflate[squareTile, 1]],  
      colorGraph[deflate[rhombTile, 1]]]

Two more starting objects: octagon and eightstar.

GraphicsArray[colorGraph[deflate[octagon, 0]],  
      colorGraph[deflate[eightstar, 0]]]

The command lineGraph has no options.

lineGraph[deflate[rhombTile, 3]]

Next example illustrates colorGraph. Same usage as above with some options (see below).

colorGraph[deflate[octagon, 1]]

The colors of the tiles could be chosen with the options squareColor and rhombColor.

colorGraph[deflate[eightstar, 2],  squareColor  ->  Orchid,  
      rhombColor  ->   Raspberry]

pointGraph draw the vertices of the tiling.

pointGraph[deflate[squareTile, 3]]

We have the following options: psize determines the size of the points (default = 0.008), pointColor specifies the color of the points; and backColor gives the color of the background.

pointGraph[deflate[octagon, 1],  
      psize  ->   0.06,   pointColor  ->  Red,  
      backColor  ->  Blue]

We have the following options: psize determines the size of the points (default = 0.008), pointColor specifies the color of the points; and backColor gives the color of the background.

Ammann A3 (The Gamma shape)

The next cell (after evaluated) produces an Ammann A3 tiling starting with the la3Tile (large A3 tile).

colorGraph[deflate[la3Tile, 12],  la3Color  ->  Red,  
      sa3Color  ->  Gold]

The uncoloured version of the same tiing is below.

lineGraph[deflate[la3Tile, 14]]

Here is how to get a rectangular picture of the same tiling.

Show[
      colorGraphA3[deflate[la3Tile, 16],  la3Color  -> Olive,  
        sa3Color  ->  Green],  
      DisplayFunction  ->  $DisplayFunction]