About the Escher Tiling Background

The background image was generated with the Escher package by Rick Mabry and Stan Wagon.  The package is based on Escher's own method of describing tilings of the Euclidean plane.  The basic elements are a small motif, described by the option Motif, and a signature, described by a matrix, which indicates how 4 copies of the small motif fit together to make a tile.  A complete description of this package may be found in the book Mathematica in Action by Stan Wagon.  Here's how I generated the image.

Needs["Escher`"] 
(* This package comes with Wagon's Book *)
EscherTiling[{{1,1},{-1,-1}}, Motif -> EscherCurves[24],
    Colors -> {GrayLevel[.9], GrayLevel[.95]}, 
    BorderLines -> {GrayLevel[0.8]}, Frame -> False]

Of course the image needs to be resized and converted to a GIF to use on a web page.  Furthermore, Mathematica includes an annoying boundary around all of its images which needs to be trimmed by hand.  But the result looks quite nice.  Here are a few more images.

(* The same image as above, but tiled *)
EscherTiling[{{1,1},{-1,-1}}, Motif -> EscherCurves[24], 
    Size -> {8,6}]

(* An image using Escher's first basic motif *)
EscherTiling[{{a,1},{-a,-1}}, Size -> {8,6}, 
    MinimumColoring -> False]

(* Same signature, different motif *)
EscherTiling[{{a,1},{-a,-1}}, Motif -> Escher1942Motif,
    Size -> {8,6}, MinimumColoring -> False]