 Explanation
 Pictures
 Software
 Wallpaper
 Thanks
 Various Links
Explanation
Quasicrystals are tilings of the plane which are not periodic,
but still can be symmetric. The most common form is called a Penrose tiling
after the mathematician who invented it, and this tiling can have fivefold
symmetry. These patterns can be generated typically by putting together
two different tiles; a single tile alone will not work (for unusual
symmetries, at least.)
Pictures
I have several pictures based on quasicrystalline tiling. If you'd
like to look at a gallery of all of my pictures, click on this text.
Here are clips from the pictures which specifically show
quasi crystals; click to see the larger image.
Pictures of quasicrystals 
Cellular automata done
on quasicrystals



Software
Click here to get a copy of the software that created this picture.
Quasicrystal wallpaper

This is the image I am using as
a background tile for this web page.
It is cut from a larger image, below.
In most browsers, if you rightclick on
the image at the right, you can download
the tile.
 

Click here for
more mathematical wallpaper tiles
This is made from a quasicrystalline tiling (a Penrose tiling). The fainter
gray lines are the underlying tiling, consisting of fat and skinny
diamonds. The black lines have been drawn by connecting the midpoints
of the edges of the tiles. I have not connected all of the midpoints;
if you look closely, you can see that the midpoints are connected
between the edges extending from the obtuse angle of each tile. For the
background tile of my home page (and this page), I clipped a symmetric
region from this pattern.
The bars on this page are made from a similar sort of pattern.
Thanks to...
When I took Mike Marder's
Solid State physics class, he assigned for homework the problem of
generating a quasicrystalline tiling with a computer program. Ever
since then I've been having fun making quasicrystal pictures. Later I
went to the 8th Annual
Complex Systems Summer School held at the Santa Fe Institute, where
Dave
Ardell
suggested doing
cellular automata on quasicrystals. This resulted in an
additional burst of programming and many more pictures.
Current address:
Eric R. Weeks
weeks/physics.emory.edu
Department of Physics
Emory University
Atlanta, GA 303222430